A054497 Number of symmetric nonnegative integer 7 X 7 matrices with sum of elements equal to 4*n, under action of dihedral group D_4.

1, 7, 31, 105, 300, 756, 1732, 3676, 7330, 13870, 25102, 43714, 73612, 120340, 191620, 298012, 453739, 677677, 994565, 1436435, 2044328, 2870296, 3979768, 5454280, 7394660, 9924668, 13195196, 17389028, 22726280, 29470520, 37935704, 48493928, 61584149

Offset: 0

Author

Vladeta Jovovic, May 14 2000

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-18,14,25,-63,36,36,-63,25,14,-18,7,-1).

Crossrefs

Cf. A001753, A038163.

Programs

Mathematica

CoefficientList[Series[1/((1-x)^7(1-x^2)^3),{x,0,30}],x] (* Harvey P. Dale, Feb 03 2012 *)

PARI

Vec(1 / ((1-x)^7*(1-x^2)^3) + O(x^40)) \\ Colin Barker, Jan 15 2017

Formula

G.f.: 1 / ((1-x)^7 * (1-x^2)^3).

a(0)=1, a(1)=7, a(2)=31, a(3)=105, a(4)=300, a(5)=756, a(6)=1732, a(7)=3676, a(8)=7330, a(9)=13870, a(10)=25102, a(11)=43714, a(12)=73612, a(n) = 7*a(n-1) - 18*a(n-2) + 14*a(n-3) + 25*a(n-4) - 63*a(n-5) + 36*a(n-6) + 36*a(n-7) - 63*a(n-8) + 25*a(n-9) + 14*a(n-10) - 18*a(n-11) + 7*a(n-12) - a(n-13). - Harvey P. Dale, Feb 03 2012

a(n) = ((2835*(4017+79*(-1)^n) + 18*(1513217+4095*(-1)^n)*n + 90*(284609+63*(-1)^n)*n^2 + 12771104*n^3 + 3787056*n^4 + 701400*n^5 + 81900*n^6 + 5856*n^7 + 234*n^8 + 4*n^9)) / 11612160. - Colin Barker, Jan 15 2017