cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A054498 #17 Jan 15 2017 08:25:27
%S A054498 1,4,16,44,116,260,560,1100,2090,3740,6512,10868,17732,28028,43472,
%T A054498 65780,97955,143000,205920,291720,408408,563992,770848,1041352,
%U A054498 1394068,1847560,2428960,3165400,4095640,5258440,6708064,8498776,10705189,13401916,16689904
%N 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.
%D A054498 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.)
%H A054498 Alois P. Heinz, <a href="/A054498/b054498.txt">Table of n, a(n) for n = 0..1000</a>
%H A054498 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-20,20,36,-64,-20,90,-20,-64,36,20,-20,0,4,-1).
%F A054498 G.f.: 1 / ((1-x)^4 * (1-x^2)^6).
%F A054498 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
%o A054498 (PARI) Vec(1 / ((1-x)^4*(1-x^2)^6) + O(x^40)) \\ _Colin Barker_, Jan 15 2017
%Y A054498 Cf. A001753, A038163.
%Y A054498 Column k=4 of A210391. - _Alois P. Heinz_, Mar 22 2012
%K A054498 easy,nonn
%O A054498 0,2
%A A054498 _Vladeta Jovovic_, May 14 2000