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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.
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
0,2
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
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).
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
PROG
(PARI) Vec(1 / ((1-x)^4*(1-x^2)^6) + O(x^40)) \\ Colin Barker, Jan 15 2017
CROSSREFS
Column k=4 of A210391. - Alois P. Heinz, Mar 22 2012
Sequence in context: A217873 A289086 A018210 * A360278 A293629 A217553
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, May 14 2000
STATUS
approved