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%I #15 Jul 12 2021 14:32:53
%S 1,96,817,137712,1177393,198579888,1697799169,286352060064,
%T 2448225223585,412919472031680,3530339074609681,595429592317621776,
%U 5090746497361935697,858609059202538568592,7340852918856836664673,1238113667940468298287168,10585504818245061108522049
%N Indices of centered pentagonal numbers (A005891) which are also centered octagonal numbers (A016754).
%C Also positive integers x in the solutions to 5*x^2 - 8*y^2 - 5*x + 8*y = 0, the corresponding values of y being A253411.
%H Colin Barker, <a href="/A253410/b253410.txt">Table of n, a(n) for n = 1..633</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1442,-1442,-1,1).
%F a(n) = a(n-1) + 1442*a(n-2) - 1442*a(n-3) - a(n-4) + a(n-5).
%F G.f.: x*(95*x^3 + 721*x^2 - 95*x - 1) / ((x-1)*(x^2 - 38*x + 1)*(x^2 + 38*x + 1)).
%e 96 is in the sequence because the 96th centered pentagonal number is 22801, which is also the 76th centered octagonal number.
%t LinearRecurrence[{1,1442,-1442,-1,1},{1,96,817,137712,1177393},20] (* _Harvey P. Dale_, Jul 12 2021 *)
%o (PARI) Vec(x*(95*x^3+721*x^2-95*x-1)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))
%Y Cf. A005891, A016754, A253411, A253579.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Dec 31 2014