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 A048902 Indices of heptagonal numbers (A000566) which are also hexagonal. 3
 1, 221, 71065, 22882613, 7368130225, 2372515049741, 763942477886281, 245987105364332645, 79207083984837225313, 25504435056012222218045, 8212348880951950716985081, 2644350835231472118646977941 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (2 + sqrt(5))^4 = 161 + 72*sqrt(5). - Ant King, Dec 26 2011 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 Eric Weisstein's World of Mathematics, Heptagonal hexagonal number. Index entries for linear recurrences with constant coefficients, signature (323,-323,1). FORMULA G.f.: -x*(1 - 102*x + 5*x^2) / ( (x-1)*(x^2 - 322*x + 1) ). - R. J. Mathar, Dec 21 2011 From Ant King, Dec 26 2011: (Start) a(n) = 322*a(n-1) - a(n-2) - 96. a(n) = (1/20)*((sqrt(5)+1)*(sqrt(5)+2)^(4*n-3) + (sqrt(5)-1)*(sqrt(5)-2)^(4*n-3) + 6). a(n) = ceiling((1/20)*(sqrt(5)+1)*(sqrt(5)+2)^(4*n-3)). (End) MATHEMATICA LinearRecurrence[{323, -323, 1}, {1, 221, 71065}, 12]; (* Ant King, Dec 26 2011 *) PROG (MAGMA) I:=[1, 221, 71065]; [n le 3 select I[n] else 323*Self(n-1)-323*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Dec 28 2011 CROSSREFS Cf. A048901, A048903. Sequence in context: A220737 A220723 A011816 * A210135 A013548 A300517 Adjacent sequences:  A048899 A048900 A048901 * A048903 A048904 A048905 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified January 27 15:07 EST 2022. Contains 350607 sequences. (Running on oeis4.)