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%I #10 Feb 23 2017 22:22:51
%S 0,1,120,3654,45760,333375,1703016,6784540,22500864,64836045,
%T 167167000,393877506,861456960,1769830699,3447273480,6412923000,
%U 11461636096,19776716505,33076889784,53804808190,85365336000,132422893911,201268229800,300266132244,440396812800
%N Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to row permutations.
%C Cycle index of symmetry group is (3*s(2)^3*s(1)^3 + 2*s(3)^3 + s(1)^9)/6.
%H Colin Barker, <a href="/A282612/b282612.txt">Table of n, a(n) for n = 0..1000</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) = n^3*(n^3+2)*(n+1)*(n^2-n+1)/6.
%F G.f.: x*(1 + 110*x + 2499*x^2 + 14500*x^3 + 26015*x^4 + 14934*x^5 + 2365*x^6 + 56*x^7) / (1 - x)^10. - _Colin Barker_, Feb 23 2017
%e The number of 3 X 3 binary matrices up to row permutations is 120.
%t Table[(3n^6+2n^3+n^9)/6, {n, 0, 24}]
%o (PARI) concat(0, Vec(x*(1 + 110*x + 2499*x^2 + 14500*x^3 + 26015*x^4 + 14934*x^5 + 2365*x^6 + 56*x^7) / (1 - x)^10 + O(x^30))) \\ _Colin Barker_, Feb 23 2017
%Y Cf. A282613, A282614, A217331, A168555. A037270 (2x2 version.)
%K nonn,easy
%O 0,3
%A _David Nacin_, Feb 19 2017
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