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%I #13 Feb 04 2016 16:18:02
%S 1,76,646,108871,930811,156991186,1342228096,226381180621,
%T 1935491982901,326441505463576,2790978097114426,470728424497295251,
%U 4024588480547018671,678790061683594287646,5803453797970703808436,978814798219318465489561,8368576352085274344745321
%N Indices of centered octagonal numbers (A016754) which are also centered pentagonal numbers (A005891).
%C Also positive integers y in the solutions to 5*x^2 - 8*y^2 - 5*x + 8*y = 0, the corresponding values of x being A253410.
%H Colin Barker, <a href="/A253411/b253411.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*(x^4 + 75*x^3 - 872*x^2 + 75*x + 1) / ((x-1)*(x^2 - 38*x + 1)*(x^2 + 38*x + 1)).
%e 76 is in the sequence because the 76th centered octagonal number is 22801, which is also the 96th centered pentagonal number.
%t LinearRecurrence[{1,1442,-1442,-1,1},{1,76,646,108871,930811},20] (* _Harvey P. Dale_, Feb 04 2016 *)
%o (PARI) Vec(-x*(x^4+75*x^3-872*x^2+75*x+1)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))
%Y Cf. A005891, A016754, A253410, A253579.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Dec 31 2014
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