A244878 Number of 6 X 6 traceless symmetric magic squares with magic sum n.

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

Colin Barker, Table of n, a(n) for n = 0..1000

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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

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

Adjacent sequences: A244875 A244876 A244877 * A244879 A244880 A244881

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 08 2014

Status

approved