1:e																			1:e
	Put only in one Integer in a and d.
									B . .  . .   . .		A B C D E F G H I J K L M N O					Special Magic Square one n = 15												B . .  . .   . .		A B C D E F G H I J K L M N O
a =	1		a = 0,1,2,3……		[-∞ < a < ∞]			2:e	:																		2:e	:
									:																			:
d =	1		d = 1,2,3,4……		num: [d ≠ 0]											Partiell Bimagic Square n15:1,a																		MS Matrix n15:1,b
									17	39	56	72	88	105	106	123	143	155	172	194	205	214	6	1695	254815		B2	C9	D11	E12	F13	G15	H1	I3	J8	K5	L7	M14	N10	O4	A6
Σn14 =	1695		Σy = sum(A1:N1) /n						53	73	82	104	115	124	140	152	174	191	207	216	15	16	33	1695	254815		D8	E13	F7	G14	H10	I4	J5	K2	L9	M11	N12	O6	A15	B1	C3
									89	100	109	125	142	159	176	192	201	212	1	18	38	58	75	1695	254815		F14	G10	H4	I5	J7	K9	L11	M12	N6	O2	A1	B3	C8	D13	E15
Σn15 =	1695		Σ(n:a,d) = ½·n·[2·a + d·(n^2 -1)]						110	127	149	161	177	186	197	219	3	23	43	60	61	85	94	1695	254815		H5	I7	J14	K11	L12	M6	N2	O9	A3	B8	C13	D15	E1	F10	G4
			[Hunter and Madachy 1975]						146	158	178	195	196	213	4	20	37	59	70	87	96	107	129	1695	254815		J11	K8	L13	M15	N1	O3	A4	B5	C7	D14	E10	F12	G6	H2	I9
	MS order n =	15							180	181	198	218	5	22	44	55	64	81	92	114	131	147	163	1695	254815		L15	M1	N3	O8	A5	B7	C14	D10	E4	F6	G2	H9	I11	J12	K13
				The Key n15					199	215	2	24	41	57	66	90	91	108	128	148	157	179	190	1695	254815		N4	O5	A2	B9	C11	D12	E6	F15	G1	H3	I8	J13	K7	L14	M10
			A1	=	1				9	26	42	51	62	76	93	113	133	150	164	175	184	200	217	1695	254815		A9	B11	C12	D6	E2	F1	G3	H8	I13	J15	K14	L10	M4	N5	O7
			A2	=	2				36	47	69	78	98	118	135	136	160	169	185	202	224	11	27	1695	254815		C6	D2	E9	F3	G8	H13	I15	J1	K10	L4	M5	N7	O14	A11	B12
			A3	=	3				63	79	95	112	134	145	162	171	182	204	221	8	28	45	46	1695	254815		E3	F4	G5	H7	I14	J10	K12	L6	M2	N9	O11	A8	B13	C15	D1
			A4	=	4				97	119	130	139	156	167	189	206	222	13	30	31	48	68	80	1695	254815		G7	H14	I10	J4	K6	L2	M9	N11	O12	A13	B15	C1	D3	E8	F5
			A5	=	5				132	141	165	166	183	203	223	7	29	40	49	65	77	99	116	1695	254815		I12	J6	K15	L1	M3	N8	O13	A7	B14	C10	D4	E5	F2	G9	H11
			A6	=	6				151	168	188	208	225	14	25	34	50	67	84	101	117	126	137	1695	254815		K1	L3	M8	N13	O15	A14	B10	C4	D5	E7	F9	G11	H12	I6	J2
			A7	=	7				193	210	211	10	19	35	52	74	86	102	111	122	144	153	173	1695	254815		M13	N15	O1	A10	B4	C5	D7	E14	F11	G12	H6	I2	J9	K3	L8
			A8	=	8				220	12	21	32	54	71	83	103	120	121	138	154	170	187	209	1695	254815		O10	A12	B6	C2	D9	E11	F8	G13	H15	I1	J3	K4	L5	M7	N14
			A9	=	9				1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695
			A10	=	10											254815								1695			B2	E13	H4	K11	N1	B7	E6	H8	K10	N9	B15	E5	H12	K3	N14
			A11	=	11																						O10	N15	M8	L1	K6	J10	I15	H8	G1	F6	E10	D15	C8	B1	A6
			A12	=	12
			A13	=	13				1:e																			1:e
			A14	=	14
			A15	=	15				L . .  . .   . .		A B C D E F G H I J K L M N O					Special Magic Square two n = 15												L . .  . .   . .		A B C D E F G H I J K L M N O
			B1	=	16			7:e	:																		7:e	:
			B2	=	17				:																			:
			B3	=	18											Partiell Bimagic Square n15:2,a																		MS Matrix n15:2,b
			B4	=	19				180	181	198	218	5	22	44	55	64	81	92	114	131	147	163	1695	254815		L15	M1	N3	O8	A5	B7	C14	D10	E4	F6	G2	H9	I11	J12	K13
			B5	=	20				53	73	82	104	115	124	140	152	174	191	207	216	15	16	33	1695	254815		D8	E13	F7	G14	H10	I4	J5	K2	L9	M11	N12	O6	A15	B1	C3
			B6	=	21				151	168	188	208	225	14	25	34	50	67	84	101	117	126	137	1695	254815		K1	L3	M8	N13	O15	A14	B10	C4	D5	E7	F9	G11	H12	I6	J2
			B7	=	22				36	47	69	78	98	118	135	136	160	169	185	202	224	11	27	1695	254815		C6	D2	E9	F3	G8	H13	I15	J1	K10	L4	M5	N7	O14	A11	B12
			B8	=	23				146	158	178	195	196	213	4	20	37	59	70	87	96	107	129	1695	254815		J11	K8	L13	M15	N1	O3	A4	B5	C7	D14	E10	F12	G6	H2	I9
			B9	=	24				17	39	56	72	88	105	106	123	143	155	172	194	205	214	6	1695	254815		B2	C9	D11	E12	F13	G15	H1	I3	J8	K5	L7	M14	N10	O4	A6
			B10	=	25				132	141	165	166	183	203	223	7	29	40	49	65	77	99	116	1695	254815		I12	J6	K15	L1	M3	N8	O13	A7	B14	C10	D4	E5	F2	G9	H11
			B11	=	26				9	26	42	51	62	76	93	113	133	150	164	175	184	200	217	1695	254815		A9	B11	C12	D6	E2	F1	G3	H8	I13	J15	K14	L10	M4	N5	O7
			B12	=	27				110	127	149	161	177	186	197	219	3	23	43	60	61	85	94	1695	254815		H5	I7	J14	K11	L12	M6	N2	O9	A3	B8	C13	D15	E1	F10	G4
			B13	=	28				220	12	21	32	54	71	83	103	120	121	138	154	170	187	209	1695	254815		O10	A12	B6	C2	D9	E11	F8	G13	H15	I1	J3	K4	L5	M7	N14
			B14	=	29				97	119	130	139	156	167	189	206	222	13	30	31	48	68	80	1695	254815		G7	H14	I10	J4	K6	L2	M9	N11	O12	A13	B15	C1	D3	E8	F5
			B15	=	30				199	215	2	24	41	57	66	90	91	108	128	148	157	179	190	1695	254815		N4	O5	A2	B9	C11	D12	E6	F15	G1	H3	I8	J13	K7	L14	M10
			C1	=	31				89	100	109	125	142	159	176	192	201	212	1	18	38	58	75	1695	254815		F14	G10	H4	I5	J7	K9	L11	M12	N6	O2	A1	B3	C8	D13	E15
			C2	=	32				193	210	211	10	19	35	52	74	86	102	111	122	144	153	173	1695	254815		M13	N15	O1	A10	B4	C5	D7	E14	F11	G12	H6	I2	J9	K3	L8
			C3	=	33				63	79	95	112	134	145	162	171	182	204	221	8	28	45	46	1695	254815		E3	F4	G5	H7	I14	J10	K12	L6	M2	N9	O11	A8	B13	C15	D1
			C4	=	34				1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695
			C5	=	35											254815								1695			L15	E13	M8	F3	N1	G15	O13	H8	A3	I1	B15	J13	C8	K3	D1
			C6	=	36																						E3	N15	H4	B9	K6	E11	N2	H8	B14	K5	E10	N7	H12	B1	K13
			C7	=	37
			C8	=	38											Bimagic Square n15:3,a																		MS Matrix n15:3,b
			C9	=	39				63	169	214	129	132	144	38	93	84	216	23	48	83	215	44	1695	254815		E3	L4	O4	I9	I12	J9	C8	G3	F9	O6	B8	D3	F8	O5	C14
			C10	=	40				28	160	194	146	141	102	58	217	101	16	43	31	187	179	92	1695	254815		B13	K10	M14	J11	J6	G12	D13	O7	G11	B1	C13	C1	M7	L14	G2
			C11	=	41				46	185	106	107	99	52	18	164	126	53	177	189	220	148	5	1695	254815		D1	M5	H1	H2	G9	D7	B3	K14	I6	D8	L12	M9	O10	J13	A5
			C12	=	42				204	202	155	59	65	86	1	150	67	15	61	156	170	190	114	1695	254815		N9	N7	K5	D14	E5	F11	A1	J15	E7	A15	E1	K6	L5	M10	H9
			C13	=	43				8	224	172	96	40	111	75	200	25	191	60	68	121	157	147	1695	254815		A8	O14	L7	G6	C10	H6	E15	N5	B10	M11	D15	E8	I1	K7	J12
			C14	=	44				162	98	205	4	116	19	176	175	137	33	197	30	154	108	81	1695	254815		K12	G8	N10	A4	H11	B4	L11	L10	J2	C3	N2	B15	K4	H3	F6
			C15	=	45				45	135	88	87	77	122	212	184	117	73	3	13	209	199	131	1695	254815		C15	I15	F13	F12	F2	I2	O2	M4	H12	E13	A3	A13	N14	N4	I11
			D1	=	46				171	136	123	20	7	74	192	113	34	152	219	206	103	90	55	1695	254815		L6	J1	I3	B5	A7	E14	M12	H8	C4	K2	O9	N11	G13	F15	D10
			D2	=	47				95	27	17	213	223	153	109	42	14	104	149	139	138	91	181	1695	254815		G5	B12	B2	O3	O13	K3	H4	C12	A14	G14	J14	J4	J3	G1	M1
			D3	=	48				145	118	72	196	29	193	89	51	50	207	110	222	21	128	64	1695	254815		J10	H14	E12	N1	B14	M13	F14	D6	D5	N12	H5	O12	B6	I8	E4
			D4	=	49				79	69	105	158	166	35	201	26	151	115	186	130	54	2	218	1695	254815		F4	E9	G15	K8	L1	C5	N6	B11	K1	H10	M6	I10	D9	A2	O8
			D5	=	50				112	36	56	70	165	211	159	76	225	140	161	167	71	24	22	1695	254815		H7	C6	D11	E10	K15	O1	K9	F1	O15	J5	K11	L2	E11	B9	B7
			D6	=	51				221	78	6	37	49	173	100	62	208	174	127	119	120	41	180	1695	254815		O11	F3	A6	C7	D4	L8	G10	E2	N13	L9	I7	H14	H15	C11	L15
			D7	=	52				134	47	39	195	183	210	125	9	168	124	85	80	32	66	198	1695	254815		I14	D2	C9	M15	M3	N15	I5	A9	L3	I4	F10	F5	C2	E6	N3
			D8	=	53				182	11	143	178	203	10	142	133	188	82	94	97	12	57	163	1695	254815		M2	A11	J8	L13	N8	A10	J7	I13	M8	F7	G4	G7	A12	D12	K13
			D9	=	54				1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	1695	254815
			D10	=	55				254815	254815	254815	254815	254815	254815	254815	254815	254815	254815	254815	254815	254815	254815	254815	1695	254815		Bimagic Square constructor: Chen Qin-Wu, 2006. No panmagic Square of odd n = 15,
			D11	=	56																						because formula:  12k+3, if k=1
			D12	=	57
			D13	=	58
			D14	=	59
			D15	=	60
			E1	=	61
			E2	=	62
			E3	=	63
			E4	=	64
			E5	=	65
			E6	=	66
			E7	=	67
			E8	=	68
			E9	=	69
			E10	=	70
			E11	=	71
			E12	=	72
			E13	=	73
			E14	=	74
			E15	=	75
			F1	=	76
			F2	=	77
			F3	=	78
			F4	=	79
			F5	=	80
			F6	=	81
			F7	=	82
			F8	=	83
			F9	=	84
			F10	=	85
			F11	=	86
			F12	=	87
			F13	=	88
			F14	=	89
			F15	=	90
			G1	=	91
			G2	=	92
			G3	=	93
			G4	=	94
			G5	=	95
			G6	=	96
			G7	=	97
			G8	=	98
			G9	=	99
			G10	=	100
			G11	=	101
			G12	=	102
			G13	=	103
			G14	=	104
			G15	=	105
			H1	=	106
			H2	=	107
			H3	=	108
			H4	=	109
			H5	=	110
			H6	=	111
			H7	=	112
			H8	=	113
			H9	=	114
			H10	=	115
			H11	=	116
			H12	=	117
			H13	=	118
			H14	=	119
			H15	=	120
			I1	=	121
			I2	=	122
			I3	=	123
			I4	=	124
			I5	=	125
			I6	=	126
			I7	=	127
			I8	=	128
			I9	=	129
			I10	=	130
			I11	=	131
			I12	=	132
			I13	=	133
			I14	=	134
			I15	=	135
			J1	=	136
			J2	=	137
			J3	=	138
			J4	=	139
			J5	=	140
			J6	=	141
			J7	=	142
			J8	=	143
			J9	=	144
			J10	=	145
			J11	=	146
			J12	=	147
			J13	=	148
			J14	=	149
			J15	=	150
			K1	=	151
			K2	=	152
			K3	=	153
			K4	=	154
			K5	=	155
			K6	=	156
			K7	=	157
			K8	=	158
			K9	=	159
			K10	=	160
			K11	=	161
			K12	=	162
			K13	=	163
			K14	=	164
			K15	=	165
			L1	=	166
			L2	=	167
			L3	=	168
			L4	=	169
			L5	=	170
			L6	=	171
			L7	=	172
			L8	=	173
			L9	=	174
			L10	=	175
			L11	=	176
			L12	=	177
			L13	=	178
			L14	=	179
			L15	=	180
			M1	=	181
			M2	=	182
			M3	=	183
			M4	=	184
			M5	=	185
			M6	=	186
			M7	=	187
			M8	=	188
			M9	=	189
			M10	=	190
			M11	=	191
			M12	=	192
			M13	=	193
			M14	=	194
			M15	=	195
			N1	=	196
			N2	=	197
			N3	=	198
			N4	=	199
			N5	=	200
			N6	=	201
			N7	=	202
			N8	=	203
			N9	=	204
			N10	=	205
			N11	=	206
			N12	=	207
			N13	=	208
			N14	=	209
			N15	=	210
			O1	=	211
			O2	=	212
			O3	=	213
			O4	=	214
			O5	=	215
			O6	=	216
			O7	=	217
			O8	=	218
			O9	=	219
			O10	=	220
			O11	=	221
			O12	=	222
			O13	=	223
			O14	=	224
			O15	=	225
			MQM copy right © 2019