A054549 Number of symmetric nonnegative integer 9 X 9 matrices with sum of elements equal to 4*n, under action of dihedral group D_4.

1, 9, 51, 219, 786, 2466, 6974, 18126, 43929, 100321, 217683, 451707, 901128, 1735752, 3239928, 5878328, 10393902, 17950878, 30340682, 50273658, 81787476, 130811124, 205935756, 319456044, 488764246, 738197766, 1101468114, 1624826306, 2371158504, 3425244456

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (9,-30,30,75,-243,152,360,-690,130,780,-780,-130,690,-360,-152,243,-75,-30,30,-9,1).

Formula

G.f.: 1 / ((1-x)^9 * (1-x^2)^6).

a(n) = ((85135050*(256719+5425*(-1)^n) + 1890*(30592018355+141137997*(-1)^n)*n + 9*(7020005494399+6456074625*(-1)^n)*n^2 + 15288*(2534162507+393525*(-1)^n)*n^3 + 455*(33274853083+654885*(-1)^n)*n^4 + 126126*(31995443+45*(-1)^n)*n^5 + 763179408992*n^6 + 104737240608*n^7 + 10538322080*n^8 + 777020244*n^9 + 41479438*n^10 + 1559376*n^11 + 39130*n^12 + 588*n^13 + 4*n^14)) / 22317642547200. - Colin Barker, Jan 15 2017

Prog

(PARI) Vec(1 / ((1-x)^9*(1-x^2)^6) + O(x^40)) \\ Colin Barker, Jan 15 2017

Crossrefs

Cf. A001753, A038163.

Sequence in context: A330805 A282877 A055900 * A005746 A220236 A345954

Adjacent sequences: A054546 A054547 A054548 * A054550 A054551 A054552

Keyword

easy,nonn

Author

Vladeta Jovovic, May 14 2000

Status

approved