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 A253470 Indices of centered triangular numbers (A005448) which are also centered pentagonal numbers (A005891). 2
 1, 5, 36, 280, 2201, 17325, 136396, 1073840, 8454321, 66560725, 524031476, 4125691080, 32481497161, 255726286205, 2013328792476, 15850904053600, 124793903636321, 982500325036965, 7735208696659396, 60899169248238200, 479458145289246201, 3774765993065731405 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also indices of pentagonal numbers (A000326) which are also centered pentagonal numbers (A005891). Also positive integers x in the solutions to 3*x^2 - 5*y^2 - 3*x + 5*y = 0, the corresponding values of y being A182432. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (9,-9,1). FORMULA a(n) = 9*a(n-1)-9*a(n-2)+a(n-3). G.f.: x*(4*x-1) / ((x-1)*(x^2-8*x+1)). a(n) = (6-(4-sqrt(15))^n*(3+sqrt(15))+(-3+sqrt(15))*(4+sqrt(15))^n)/12. - Colin Barker, Mar 03 2016 EXAMPLE 5 is in the sequence because the 5th centered triangular number is 31, which is also the 4th centered pentagonal number. PROG (PARI) Vec(x*(4*x-1)/((x-1)*(x^2-8*x+1)) + O(x^100)) CROSSREFS Cf. A005448, A005891, A182432, A253654. Sequence in context: A285392 A327091 A201351 * A188899 A052203 A332624 Adjacent sequences: A253467 A253468 A253469 * A253471 A253472 A253473 KEYWORD nonn,easy AUTHOR Colin Barker, Jan 01 2015 STATUS approved

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Last modified February 23 09:42 EST 2024. Contains 370276 sequences. (Running on oeis4.)