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 A282613 Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to rotations. 13
 0, 1, 140, 4995, 65824, 489125, 2521476, 10092775, 33562880, 96870249, 250025500, 589527851, 1290008160, 2651218765, 5165397524, 9611031375, 17180133376, 29647326545, 49590297900, 80672546899, 128000804000, 198571037301, 301818598180, 450289780535 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Cycle index of symmetry group (cyclic rotation group of order 4 acting on the 9 cells of the square) is (2s(4)^2*s(1) + s(2)^4*s(1) + s(1)^9)/4. 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^2+1)*(n^4-n^2+2)/4. G.f.: x*(1 + 130*x + 3640*x^2 + 22054*x^3 + 39070*x^4 + 22054*x^5 + 3640*x^6 + 130*x^7 + x^8) / (1 - x)^10. - Colin Barker, Feb 23 2017 EXAMPLE The number of 3 X 3 binary matrices up to rotations is 140. MATHEMATICA Table[(2n^3+n^5+n^9)/4, {n, 0, 24}] PROG (PARI) concat(0, Vec(x*(1 + 130*x + 3640*x^2 + 22054*x^3 + 39070*x^4 + 22054*x^5 + 3640*x^6 + 130*x^7 + x^8) / (1 - x)^10 + O(x^30))) \\ Colin Barker, Feb 23 2017 CROSSREFS Row n=3 of A343095. Cf. A282612, A282614, A217331, A168555. Cf. A006528 (2 x 2 version), A283027 (4 X 4 version). Sequence in context: A128193 A061607 A223349 * A202786 A035820 A075915 Adjacent sequences: A282610 A282611 A282612 * A282614 A282615 A282616 KEYWORD nonn,easy AUTHOR David Nacin, Feb 19 2017 STATUS approved

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Last modified February 22 02:45 EST 2024. Contains 370239 sequences. (Running on oeis4.)