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 A253922 Indices of centered pentagonal numbers (A005891) which are also octagonal numbers (A000567). 3
 1, 56, 297, 26752, 142913, 12894168, 68883529, 6214961984, 33201717825, 2995598781880, 16003159107881, 1443872397903936, 7713489488280577, 695943500190915032, 3717885930192129993, 335443323219623141248, 1792013304863118375809, 161682985848358163166264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also positive integers y in the solutions to 6*x^2 - 5*y^2 - 4*x + 5*y - 2 = 0, the corresponding values of x being A253921. LINKS Colin Barker, Table of n, a(n) for n = 1..745 Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1). FORMULA a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5). G.f.: x*(55*x^3+241*x^2-55*x-1) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)). EXAMPLE 56 is in the sequence because the 56th centered pentagonal is 7701, which is also the number 51st octagonal number. MATHEMATICA CoefficientList[Series[(55 x^3 + 241 x^2 - 55 x - 1)/((x - 1)(x^2 - 22 x + 1) (x^2 + 22 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2015 *) PROG (PARI) Vec(x*(55*x^3+241*x^2-55*x-1)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100)) (MAGMA) I:=[1, 56, 297, 26752, 142913]; [n le 5 select I[n] else Self(n-1)+482*Self(n-2)-482*Self(n-3)-Self(n-4)+Self(n-5): n in [1..25]]; // Vincenzo Librandi, Jan 20 2015 CROSSREFS Cf. A000567, A005891, A253921, A253923. Sequence in context: A205235 A205228 A110554 * A220015 A005912 A264581 Adjacent sequences:  A253919 A253920 A253921 * A253923 A253924 A253925 KEYWORD nonn,easy AUTHOR Colin Barker, Jan 19 2015 STATUS approved

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Last modified October 27 19:26 EDT 2020. Contains 338035 sequences. (Running on oeis4.)