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 A282612 Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to row permutations. 10
 0, 1, 120, 3654, 45760, 333375, 1703016, 6784540, 22500864, 64836045, 167167000, 393877506, 861456960, 1769830699, 3447273480, 6412923000, 11461636096, 19776716505, 33076889784, 53804808190, 85365336000, 132422893911, 201268229800, 300266132244, 440396812800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Cycle index of symmetry group is (3*s(2)^3*s(1)^3 + 2*s(3)^3 + s(1)^9)/6. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). FORMULA a(n) = n^3*(n^3+2)*(n+1)*(n^2-n+1)/6. 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 EXAMPLE The number of 3 X 3 binary matrices up to row permutations is 120. MATHEMATICA Table[(3n^6+2n^3+n^9)/6, {n, 0, 24}] PROG (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 CROSSREFS Cf. A282613, A282614, A217331, A168555. A037270 (2x2 version.) Sequence in context: A183266 A231129 A052722 * A231136 A222003 A139389 Adjacent sequences:  A282609 A282610 A282611 * A282613 A282614 A282615 KEYWORD nonn,easy AUTHOR David Nacin, Feb 19 2017 STATUS approved

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Last modified February 29 04:32 EST 2020. Contains 332353 sequences. (Running on oeis4.)