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A058001 Number of 3 X 3 matrices with entries mod n, up to row and column permutation. 6

%I #23 Jun 30 2022 08:36:30

%S 1,36,738,8240,57675,289716,1144836,3780288,10865205,27969700,

%T 65834406,143887536,295467263,575308020,1069960200,1911933696,

%U 3298486761,5516122788,8972008810,14233690800,22078652211,33555443636,50058302988,73417387200,106006948125

%N Number of 3 X 3 matrices with entries mod n, up to row and column permutation.

%C Number of k X l matrices with entries mod n, up to row and column permutation is Z(S_k X S_l; n,n,...) where Z(S_k X S_l; x_1,x_2,...) is cycle index of Cartesian product of symmetric groups S_k and S_l of degree k and l, respectively.

%H Alois P. Heinz, <a href="/A058001/b058001.txt">Table of n, a(n) for n = 1..1000</a>

%H Marko R. Riedel, <a href="https://math.stackexchange.com/questions/2056708/">Number of equivalence classes of matrices</a>, Math Stackexchange.

%H Marko R. Riedel, <a href="/A058001/a058001.html.txt">Computing the cycle index for arbitary k x l matrices using Maple</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F a(n) = (1/3!^2)*(n^9 + 6*n^6 + 9*n^5 + 8*n^3 + 12*n^2).

%F G.f.: x*(12*x^7+369*x^6+2514*x^5+4375*x^4+2360*x^3+423*x^2+26*x+1) / (x-1)^10. - _Colin Barker_, Jul 09 2013

%Y Cf. A058002, A058003, A058004, A002724, A052271, A052272.

%Y Row n=3 of A246106.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Nov 04 2000

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Last modified March 29 09:14 EDT 2024. Contains 371268 sequences. (Running on oeis4.)