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 A243208 Number of inequivalent (mod D_3) ways to place 3 points on a triangular grid of side n so that they are not vertices of an equilateral triangle with sides parallel to the grid. 5
 0, 3, 20, 77, 223, 552, 1196, 2380, 4388, 7657, 12710, 20301, 31297, 46892, 68426, 97674, 136596, 187713, 253770, 338217, 444773, 578018, 742852, 945210, 1191398, 1488949, 1845824, 2271415, 2775605, 3369930, 4066480, 4879238, 5822810, 6913947, 8170098, 9611127, 11257671 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS Heinrich Ludwig, Table of n, a(n) for n = 2..1000 Index entries for linear recurrences with constant coefficients, signature (3,0,-7,3,6,0,-6,-3,7,0,-3,1). FORMULA a(n) = (n^6 + 3*n^5 - 3*n^4 - 2*n^3 - 48*n^2 + 48*n)/288 + IF(MOD(n, 2) = 1)*(3*n^2 - 9*n - 1)/32 + IF(MOD(n, 3) = 1)*2/9. G.f.: x^3*(-3 - 11*x - 17*x^2 - 13*x^3 - 14*x^4 - x^5 - 2*x^6 + x^7) / ((-1+x)^7 * (1+x)^3 * (1+x+x^2)). - Vaclav Kotesovec, Jun 02 2014 a(n) = 3*a(n-1) - 7*a(n-3) + 3*a(n-4) + 6*a(n-5) - 6*a(n-7) - 3*a(n-8) + 7*a(n-9) - 3*a(n-11) + a(n-12). - Vaclav Kotesovec, Jun 02 2014 MATHEMATICA Drop[CoefficientList[Series[x^3*(-3 - 11*x - 17*x^2 - 13*x^3 - 14*x^4 - x^5 - 2*x^6 + x^7) / ((-1+x)^7 * (1+x)^3 * (1+x+x^2)), {x, 0, 50}], x], 2] (* Vaclav Kotesovec, Jun 02 2014 *) CROSSREFS Cf. A243207, A243212, A001399, A227327, A243209, A243210. Sequence in context: A196741 A196899 A006411 * A373499 A129549 A171673 Adjacent sequences: A243205 A243206 A243207 * A243209 A243210 A243211 KEYWORD nonn,easy AUTHOR Heinrich Ludwig, Jun 01 2014 STATUS approved

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Last modified August 3 21:27 EDT 2024. Contains 374905 sequences. (Running on oeis4.)