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%I #25 Jun 27 2019 01:18:37
%S 1,8,725,8844,836265,10205584,965048701,11777234708,1113665364305,
%T 13590918647064,1285168865358885,15683908341476764,
%U 1483083756958788601,18099216635145538208,1711477370361576686285,20886480313049609614884,1975043402313502537183905
%N Indices of octagonal numbers which are also pentagonal.
%C From _Ant King_, Dec 17 2011: (Start)
%C lim_{n->infinity} a(2n+1)/a(2n) = (1/7)*(331 + 234*sqrt(2)).
%C lim_{n->infinity} a(2n)/a(2n-1) = (1/7)*(43 + 30*sqrt(2)).
%C (End)
%H Colin Barker, <a href="/A046188/b046188.txt">Table of n, a(n) for n = 1..654</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OctagonalPentagonalNumber.html">Octagonal Pentagonal Number.</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1154,-1154,-1,1).
%F From _Ant King_, Dec 17 2011: (Start)
%F a(n) = 1154*a(n-2) - a(n-4) - 384.
%F a(n) = a(n-1) + 1154*a(n-2) - 1154*a(n-3) - a(n-4) + a(n-5).
%F a(n) = (1/24)*sqrt(2)*((3-sqrt(2)*(-1)^n)*(1+sqrt(2))^(4*n-3) - (3+sqrt(2)*(-1)^n)*(1-sqrt(2))^(4*n-3) + 4*sqrt(2)).
%F a(n) = ceiling((1/24)*sqrt(2)*((3-sqrt(2)*(-1)^n)*(1+sqrt(2))^(4*n-3))).
%F G.f.: x*(1 + 7*x - 437*x^2 + 41*x^3 + 4*x^4)/((1-x)*(1 - 34*x + x^2)*(1 + 34*x + x^2)).
%F (End)
%t LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 8, 725, 8844, 836265}, 15] (* _Ant King_, Dec 17 2011 *)
%o (PARI) Vec(-x*(4*x^4+41*x^3-437*x^2+7*x+1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^50)) \\ _Colin Barker_, Jun 23 2015
%Y Cf. A046187, A046189.
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_
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