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 A254332 Indices of centered pentagonal numbers (A005891) which are also squares (A000290). 3

%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(n-1) + 38*a(n-2) - 38*a(n-3) - a(n-4) + a(n-5).

%F G.f.: x*(2*x^3 + 19*x^2 - 2*x - 1) / ((x-1)*(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^2-2*x-1) / ((x-1)*(x^2-6*x-1)*(x^2+6*x-1)) + O(x^100))

%Y Cf. A000290, A005891, A129557, A254333.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 28 2015

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Last modified July 28 04:27 EDT 2021. Contains 346317 sequences. (Running on oeis4.)