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 A046183 Octagonal triangular numbers. 3
 1, 21, 11781, 203841, 113123361, 1957283461, 1086210502741, 18793835590881, 10429793134197921, 180458407386358101, 100146872588357936901, 1732761608929974897121, 961610260163619775927681, 16637976788487211575799941, 9233381617944204500099658261, 159757851390292596620856138561 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Ant King, Oct 31 2011: (Start) limit n -> infinity, (u(2n+1)/u(2n)) = 1/25*(6937+2832*sqrt(6)). limit n -> infinity, (u(2n)/u(2n-1)) = 1/25*(217+88*sqrt(6)). (End) Intersection of A000217 and A000567. - Michel Marcus, Feb 07 2015 LINKS Colin Barker, Table of n, a(n) for n = 1..500 Eric Weisstein's World of Mathematics, Octagonal Triangular Number. Index entries for linear recurrences with constant coefficients, signature (1,9602,-9602,-1,1). FORMULA a(n+1) = 4801*a(n) + 1100 + 980*sqrt(24*a(n)^2+11*a(n)+1). G.f.: -z*(z^4+20*z^3+2158*z^2+20*z+1) / ((z-1)*(z^2-98*z+1)*(z^2+98*z+1)). - Richard Choulet, Oct 03 2007, factored by Colin Barker, Feb 07 2015 From Ant King, Oct 31 2011: (Start) a(n) = a(n-1) + 9602*a(n-2) - 9602*a(n-3) - a(n-4) + a(n-5). a(n) = 9602*a(n-2) - a(n-4) + 2200. a(n) = 1/96*((7-2*sqrt(6)*(-1)^n)*(sqrt(3)+sqrt(2))^(4*n-2)+(7+2*sqrt(6)*(-1)^n)*(sqrt(3)-sqrt(2))^(4*n-2)-22). a(n) = floor(1/96*(7-2*sqrt(6)*(-1)^n)*(sqrt(3)+sqrt(2))^(4n-2)). (End) MATHEMATICA LinearRecurrence[{1, 9602, -9602, -1, 1}, {1, 21, 11781, 203841, 113123361}, 13] (* Ant King, Oct 31 2011 *) PROG (PARI) Vec(-z*(z^4+20*z^3+2158*z^2+20*z+1)/((z-1)*(z^2-98*z+1)*(z^2+98*z+1)) + O(z^36)) \\ Joerg Arndt, Feb 07 2015, factored by Colin Barker, Feb 07 2015 CROSSREFS Cf. A046181, A046182. Sequence in context: A013726 A159358 A048914 * A203674 A250065 A180769 Adjacent sequences:  A046180 A046181 A046182 * A046184 A046185 A046186 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Richard Choulet, Oct 03 2007 STATUS approved

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