Examples of multimagic series for cubes
by Lee Morgenstern, April-May 2015.

Order 11, trimagic series, S1 = 7326, S2 = 6503046, S3 = 6494103396

    1322, 1259, 845, 717, 673, 661, 645, 573, 549, 81, 1

Order 12, trimagic series, S1 = 10374, S2 = 11954306, S3 = 15497262144

    1671, 1499, 1495, 928, 926, 924, 922, 920, 498, 369, 145, 77

Order 13, tetramagic series, S1 = 14287, S2 = 20930455, S3 = 34496004361, S4 = 60643971480547

    2184, 1355, 1238, 1912, 1606, 1552, 1522, 891, 706, 502, 442, 291, 86

Order 15, trimagic series, S1 = 25320, S2 = 56978440, S3 = 144248040000

    3371, 3283, 2939, 1774, 1773, 1772, 1770, 1766, 1762, 1758, 1750, 1005, 491, 87, 19

Order 16, pentamagic series, S1 = 32776, S2 = 89511256, S3 = 275012141056, S4 = 901269770766472, S5 = 3076709603561783296

    2,  505,  765, 1074, 1117, 1259, 1419, 1688, 2409, 2678, 2838, 2980, 3023, 3332, 3592, 4095

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