This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A254332 #19 Jul 06 2024 09:23:29
%S A254332 1,3,22,96,817,3627,31006,137712,1177393,5229411,44709910,198579888,
%T A254332 1697799169,7540806315,64471658494,286352060064,2448225223585,
%U A254332 10873837476099,92968086837718,412919472031680,3530339074609681,15680066099727723,134059916748330142
%N A254332 Indices of centered pentagonal numbers (A005891) which are also squares (A000290).
%C A254332 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 A254332 Colin Barker, <a href="/A254332/b254332.txt">Table of n, a(n) for n = 1..1000</a>
%H A254332 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,38,-38,-1,1).
%F A254332 a(n) = a(n-1) + 38*a(n-2) - 38*a(n-3) - a(n-4) + a(n-5).
%F A254332 G.f.: x*(2*x^3 + 19*x^2 - 2*x - 1) / ((x-1)*(x^2 - 6*x - 1)*(x^2 + 6*x - 1)).
%F A254332 a(n) = (1/40)*(20 - b^n*(19 + 3*b) + (3 + b)*c^n - (b^n*(3 + b) + (1 - 3*b)*c^n)*(-1)^n) with b = sqrt(10) - 3 and c = sqrt(10) + 3. - _Alan Michael Gómez Calderón_, Jul 02 2024
%e A254332 3 is in the sequence because the 3rd centered pentagonal number is 16, which is also the 4th square number.
%t A254332 LinearRecurrence[{1,38,-38,-1,1},{1,3,22,96,817},30] (* _Harvey P. Dale_, Mar 27 2017 *)
%o A254332 (PARI) Vec(x*(2*x^3+19*x^2-2*x-1) / ((x-1)*(x^2-6*x-1)*(x^2+6*x-1)) + O(x^100))
%Y A254332 Cf. A000290, A005891, A129557, A254333.
%K A254332 nonn,easy
%O A254332 1,2
%A A254332 _Colin Barker_, Jan 28 2015