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 A271996 The crystallogen sequence (a(n) = A018227(n)-4). 2
 6, 14, 32, 50, 82, 114, 164, 214, 286, 358, 456, 554, 682, 810, 972, 1134, 1334, 1534, 1776, 2018, 2306, 2594, 2932, 3270, 3662, 4054, 4504, 4954, 5466, 5978, 6556, 7134, 7782, 8430, 9152, 9874, 10674, 11474, 12356, 13238, 14206, 15174, 16232, 17290, 18442 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Terms up to 114 are the atomic numbers of the elements of group 14 in the periodic table. Those elements are also called crystallogens. LINKS Colin Barker, Table of n, a(n) for n = 2..1000 Wikipedia, Carbon group. Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1). FORMULA From Colin Barker, Jun 19 2016: (Start) a(n) = (6*(-9 + (-1)^n) + (25 + 3*(-1)^n)*n + 12*n^2 + 2*n^3)/12. a(n) = (n^3 + 6*n^2 + 14*n - 24)/6 for n even. a(n) = (n^3 + 6*n^2 + 11*n - 30)/6 for n odd. a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>7. G.f.: 2*x^2*(3 + x - x^2 - 2*x^3 + x^5) / ((1-x)^4*(1+x)^2). (End) MATHEMATICA Table[(6*(-9+(-1)^n)+(25+3*(-1)^n)*n+12*n^2+2*n^3)/12, {n, 2, 10}] (* or *) LinearRecurrence[{2, 1, -4, 1, 2, -1}, {6, 14, 32, 50, 82, 114}, 50] (* G. C. Greubel, Jun 23 2016 *) PROG (PARI) Vec(2*x^2*(3+x-x^2-2*x^3+x^5)/((1-x)^4*(1+x)^2) + O(x^100)) \\ Colin Barker, Jun 19 2016 CROSSREFS Cf. A173592, A018227. Sequence in context: A134067 A024932 A273365 * A199705 A225972 A078836 Adjacent sequences:  A271993 A271994 A271995 * A271997 A271998 A271999 KEYWORD nonn,easy AUTHOR Natan Arie' Consigli, Jun 18 2016 STATUS approved

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Last modified October 22 08:29 EDT 2018. Contains 316432 sequences. (Running on oeis4.)