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 A046189 Octagonal pentagonal numbers. 4
 1, 176, 1575425, 234631320, 2098015778145, 312461813932000, 2793956983975264801, 416109772078405066376, 3720751630955537773670465, 554139209013308662750166160, 4954977037463529073741814611905, 737954942591533222733596372781560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Ant King, Dec 16 2011: (Start) lim(n->Infinity, a(2n+1)/a(2n))=1/49*(219073+154908*sqrt(2)). lim(n->Infinity, a(2n)/a(2n-1))=1/49*(3649+2580*sqrt(2)). (End) LINKS Colin Barker, Table of n, a(n) for n = 1..327 Eric Weisstein's World of Mathematics, Octagonal Pentagonal Number. Index entries for linear recurrences with constant coefficients, signature (1,1331714,-1331714,-1,1). FORMULA From Ant King, Dec 16 2011: (Start) a(n) = 1331714*a(n-2) - a(n-4) + 249696. a(n) = a(n-1) + 1331714*a(n-2) - 1331714*a(n-3) - a(n-4) + a(n-5). a(n) = 1/96*((11-6*sqrt(2)*(-1)^n)*(1+sqrt(2))^(8*n-6)+(11+6*sqrt(2)*(-1)^n)*(1-sqrt(2))^(8*n-6)-18). a(n) = floor(1/96*(11-6*sqrt(2)*(-1)^n)*(1+sqrt(2))^(8*n-6)). G.f.: x*(1+175*x+243535*x^2+5945*x^3+40*x^4)/((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)). (End) MATHEMATICA LinearRecurrence[{1, 1331714, -1331714, -1, 1}, {1, 176, 1575425, 234631320, 2098015778145}, 11] (* Ant King, Dec 16 2011 *) PROG (PARI) Vec(x*(1+175*x+243535*x^2+5945*x^3+40*x^4)/((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 23 2015 CROSSREFS Cf. A046187, A046188. Sequence in context: A159426 A009722 A159442 * A164843 A077786 A188537 Adjacent sequences:  A046186 A046187 A046188 * A046190 A046191 A046192 KEYWORD nonn,easy,changed AUTHOR STATUS approved

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