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 A048915 9-gonal pentagonal numbers. 3
 1, 651, 180868051, 95317119801, 26472137730696901, 13950766352135999751, 3874504486629442861646551, 2041856512426320950146560501, 567078683619272811125915867157001, 298849390212849227278846377616002051, 82998544594567922836927983404875025948251 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Ant King, Dec 20 2011: (Start) lim(n->Infinity, a(2n+1)/a(2n))=1/2*(277727+60605*sqrt(21)). lim(n->Infinity, a(2n)/a(2n-1))=1/2*(527+115*sqrt(21)). (End) LINKS Colin Barker, Table of n, a(n) for n = 1..246 Eric Weisstein's World of Mathematics, Nonagonal Pentagonal Number. Index entries for linear recurrences with constant coefficients, signature (1,146361602,-146361602,-1,1). FORMULA From Ant King, Dec 20 2011: (Start) a(n) = 146361602*a(n-2)-a(n-4)+35719200. a(n) = a(n-1)+146361602*a(n-2)-146361602*a(n-3)-a(n-4)+a(n-5). a(n) = 1/336*((25+4*sqrt(21))*(5-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(4n-4)+ (25-4*sqrt(21))*(5+sqrt(21)*(-1)^n)*(2*sqrt(7)-3*sqrt(3))^(4n-4)-82). a(n) = floor(1/336*(25+4*sqrt(21))*(5-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(4n-4)). G.f.: x*(1+650*x+34505798*x^2+1210450*x^3+2301*x^4) / ((1-x)*(1-12098*x+x^2)*(1+12098*x+x^2)). (End) MATHEMATICA LinearRecurrence[{1, 146361602, -146361602, -1, 1}, {1, 651, 180868051, 95317119801, 26472137730696901}, 9] (* Ant King, Dec 20 2011 *) PROG (PARI) Vec(x*(1+650*x+34505798*x^2+1210450*x^3+2301*x^4)/((1-x)*(1-12098*x+x^2)*(1+12098*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 22 2015 CROSSREFS Cf. A048913, A048914. Sequence in context: A010087 A110850 A257715 * A257827 A261552 A002232 Adjacent sequences:  A048912 A048913 A048914 * A048916 A048917 A048918 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 18 00:55 EDT 2019. Contains 328135 sequences. (Running on oeis4.)