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A244878
Number of 6 X 6 traceless symmetric magic squares with magic sum n.
2
1, 15, 130, 760, 3355, 12043, 36935, 100135, 245870, 556580, 1177295, 2351165, 4469610, 8141210, 14284170, 24247962, 39970575, 64178685, 100639000, 154470030, 232524589, 343854445, 500269705, 717006745, 1013519780, 1414412506, 1950527645, 2660213675, 3590789540, 4800229700
OFFSET
0,2
LINKS
R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]
Index entries for linear recurrences with constant coefficients, signature (9,-35,75,-90,42,42,-90,75,-35,9,-1).
FORMULA
G.f.: (1 + 6*x + 30*x^2 + 40*x^3 + 30*x^4 + 6*x^5 + x^6) / ((1 - x)^10*(1 + x)).
a(n) = (945*(507+5*(-1)^n) + 1480896*n + 2062800*n^2 + 1747040*n^3 + 989100*n^4 + 383628*n^5 + 100800*n^6 + 17160*n^7 + 1710*n^8 + 76*n^9) / 483840. - Colin Barker, Jan 12 2017
MATHEMATICA
LinearRecurrence[{9, -35, 75, -90, 42, 42, -90, 75, -35, 9, -1}, {1, 15, 130, 760, 3355, 12043, 36935, 100135, 245870, 556580, 1177295}, 30] (* Harvey P. Dale, Jul 18 2024 *)
PROG
(PARI) Vec((1 + 6*x + 30*x^2 + 40*x^3 + 30*x^4 + 6*x^5 + x^6) / ((1 - x)^10*(1 + x)) + O(x^30)) \\ Colin Barker, Jan 12 2017
CROSSREFS
Row n=6 of A333351.
Sequence in context: A156922 A271791 A155656 * A275101 A236262 A227814
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 08 2014
STATUS
approved