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 A048924 9-gonal octagonal numbers. 3
 1, 631125, 286703855361, 130242107189808901, 59165603001256545014625, 26877395137662573622784125461, 12209701798707362366915379264832801, 5546550074879110936730454426529871893125 (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) = (sqrt(6) + sqrt(7))^8 = 227137 + 35048*sqrt(42). - Ant King, Jan 03 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..100 Eric Weisstein's World of Mathematics, Nonagonal Octagonal Number. Index entries for linear recurrences with constant coefficients, signature (454275,-454275,1). FORMULA a(n) = 454275*a(n-1) - 454275*a(n-2) + a(n-3). - Vincenzo Librandi, Dec 24 2011 From Ant King, Jan 03 2012: (Start) G.f.: x*(1 + 176850*x + 261*x^2) / ((1-x)*(1 - 454274*x + x^2)). a(n) = 454274*a(n-1) - a(n-2) + 177112. a(n) = (1/672)*((11*sqrt(7) - 9*sqrt(6))*(sqrt(6) + sqrt(7))^(8*n-5) - (11*sqrt(7) + 9*sqrt(6))*(sqrt(6) - sqrt(7))^(8*n-5) - 262). a(n) = floor((1/672)*(11*sqrt(7) - 9*sqrt(6))*(sqrt(6) + sqrt(7))^(8*n-5)). (End) MATHEMATICA LinearRecurrence[{454275, -454275, 1}, {1, 631125, 286703855361}, 30] (* Vincenzo Librandi, Dec 24 2011 *) PROG (MAGMA) I:=[1, 631125, 286703855361]; [n le 3 select I[n] else 454275*Self(n-1)-454275*Self(n-2)+Self(n-3): n in [1..10]]; // Vincenzo Librandi, Dec 24 2011 CROSSREFS Cf. A048922, A048923. Sequence in context: A172701 A119398 A252894 * A183678 A267362 A251564 Adjacent sequences:  A048921 A048922 A048923 * A048925 A048926 A048927 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 20 07:20 EDT 2019. Contains 328252 sequences. (Running on oeis4.)