Siamese method

Put number 1 in the middle of the top row. Put the numbers 2 up to n (= length of the square) each time one cell diagonal up and to the right. Put number n+1 below number n. Put the numbers n+2 up to 2n each time one cell diagonal up and to the right. Put number 2n+1 below number 2n. Etcetera ...

13x13 symmetric magic square

93	108	123	138	153	168	1	16	31	46	61	76	91
107	122	137	152	167	13	15	30	45	60	75	90	92
121	136	151	166	12	14	29	44	59	74	89	104	106
135	150	165	11	26	28	43	58	73	88	103	105	120
149	164	10	25	27	42	57	72	87	102	117	119	134
163	9	24	39	41	56	71	86	101	116	118	133	148
8	23	38	40	55	70	85	100	115	130	132	147	162
22	37	52	54	69	84	99	114	129	131	146	161	7
36	51	53	68	83	98	113	128	143	145	160	6	21
50	65	67	82	97	112	127	142	144	159	5	20	35
64	66	81	96	111	126	141	156	158	4	19	34	49
78	80	95	110	125	140	155	157	3	18	33	48	63
79	94	109	124	139	154	169	2	17	32	47	62	77

You can use this method to construct magic squares of odd order from 3x3 to infinite and you get a symmetric (but not pan)magic square.

See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29 and 31x31

13x13, Siamese method.xls

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13x13 magic square