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 A048919 Indices of 9-gonal numbers which are also heptagonal. 4
 1, 88, 12445, 1767052, 250908889, 35627295136, 5058825000373, 718317522757780, 101996029406604337, 14482717858215058024, 2056443939837131635021, 292000556739014477114908 (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) = (6 + sqrt(35))^2 = 71 + 12*sqrt(35). - Ant King, Jan 01 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 Eric Weisstein's World of Mathematics, Nonagonal Heptagonal number. Index entries for linear recurrences with constant coefficients, signature (143,-143,1). FORMULA G.f.: -x*(1 - 55*x + 4*x^2) / ( (x-1)*(x^2 - 142*x + 1) ). - R. J. Mathar, Dec 21 2011 a(n) = (50 + (25-3r)*(6+r)^(2n-1) + (25+3r)*(6-r)^(2n-1))/140, where r=sqrt(35). - Bruno Berselli, Dec 21 2011 From Ant King, Jan 01 2012: (Start) a(n) = 142*a(n-1) - a(n-2) - 50. a(n) = ceiling(1/140*(45 + 7*sqrt(35))*(6 + sqrt(35))^(2*n - 2)). (End) MATHEMATICA LinearRecurrence[{143, -143, 1}, {1, 88, 12445}, 30] (* Vincenzo Librandi, Dec 21 2011 *) PROG (MAGMA) I:=[1, 88, 12445]; [n le 3 select I[n] else 143*Self(n-1)-143*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 21 2011 (Maxima) makelist(expand((50+(25-3*sqrt(35))*(6+sqrt(35))^(2*n-1)+(25+3*sqrt(35))*(6-sqrt(35))^(2*n-1))/140), n, 1, 12); /* Bruno Berselli, Dec 21 2011 */ CROSSREFS Cf. A048920, A048921. Sequence in context: A052069 A346926 A174499 * A159718 A157460 A267917 Adjacent sequences:  A048916 A048917 A048918 * A048920 A048921 A048922 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 21 00:36 EDT 2022. Contains 353886 sequences. (Running on oeis4.)