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

1, 3, 22, 96, 817, 3627, 31006, 137712, 1177393, 5229411, 44709910, 198579888, 1697799169, 7540806315, 64471658494, 286352060064, 2448225223585, 10873837476099, 92968086837718, 412919472031680, 3530339074609681, 15680066099727723, 134059916748330142

Offset

1,2

Comments

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.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,38,-38,-1,1).

Formula

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

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

Example

3 is in the sequence because the 3rd centered pentagonal number is 16, which is also the 4th square number.

Mathematica

LinearRecurrence[{1, 38, -38, -1, 1}, {1, 3, 22, 96, 817}, 30] (* Harvey P. Dale, Mar 27 2017 *)

Prog

(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))

Crossrefs

Cf. A000290, A005891, A129557, A254333.

Sequence in context: A302272 A302723 A095663 * A009029 A009032 A221543

Adjacent sequences: A254329 A254330 A254331 * A254333 A254334 A254335

Keyword

nonn,easy

Author

Colin Barker, Jan 28 2015

Status

approved