%I
%S 1,3,22,96,817,3627,31006,137712,1177393,5229411,44709910,198579888,
%T 1697799169,7540806315,64471658494,286352060064,2448225223585,
%U 10873837476099,92968086837718,412919472031680,3530339074609681,15680066099727723,134059916748330142
%N Indices of centered pentagonal numbers (A005891) which are also squares (A000290).
%C Also positive integers y in the solutions to 2*x^2  5*y^2 + 5*y  2 = 0, the corresponding values of x being A129557.
%H Colin Barker, <a href="/A254332/b254332.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,38,38,1,1).
%F a(n) = a(n1) + 38*a(n2)  38*a(n3)  a(n4) + a(n5).
%F G.f.: x*(2*x^3 + 19*x^2  2*x  1) / ((x1)*(x^2  6*x  1)*(x^2 + 6*x  1)).
%e 3 is in the sequence because the 3rd centered pentagonal number is 16, which is also the 4th square number.
%t LinearRecurrence[{1,38,38,1,1},{1,3,22,96,817},30] (* _Harvey P. Dale_, Mar 27 2017 *)
%o (PARI) Vec(x*(2*x^3+19*x^22*x1) / ((x1)*(x^26*x1)*(x^2+6*x1)) + O(x^100))
%Y Cf. A000290, A005891, A129557, A254333.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 28 2015
