A054498 Number of symmetric nonnegative integer 8 X 8 matrices with sum of elements equal to 4*n, under action of dihedral group D_4.

1, 4, 16, 44, 116, 260, 560, 1100, 2090, 3740, 6512, 10868, 17732, 28028, 43472, 65780, 97955, 143000, 205920, 291720, 408408, 563992, 770848, 1041352, 1394068, 1847560, 2428960, 3165400, 4095640, 5258440, 6708064, 8498776, 10705189, 13401916, 16689904

Offset: 0

Author

Vladeta Jovovic, May 14 2000

Keywords

• easy
• nonn

References

• Y. Teranishi, Linear Diophantine equations and invariant theory of matrices, in Commutative algebra and combinatorics (Kyoto, 1985), pp. 259-275, Adv. Stud. Pure Math., 11, North-Holland, Amsterdam, 1987. (See p. 273.)

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,0,-20,20,36,-64,-20,90,-20,-64,36,20,-20,0,4,-1).

Crossrefs

Cf. A001753, A038163.

Column k=4 of A210391. - Alois P. Heinz, Mar 22 2012

Programs

PARI

Vec(1 / ((1-x)^4*(1-x^2)^6) + O(x^40)) \\ Colin Barker, Jan 15 2017

Formula

G.f.: 1 / ((1-x)^4 * (1-x^2)^6).

a(n) = ((8+n)*(2835*(1739+309*(-1)^n) + 576*(15259+1029*(-1)^n)*n + 36*(166171+3717*(-1)^n)*n^2 + 448*(4661+27*(-1)^n)*n^3 + 14*(29749+27*(-1)^n)*n^4 + 49280*n^5 + 3416*n^6 + 128*n^7 + 2*n^8)) / 46448640. - Colin Barker, Jan 15 2017