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A254332 Indices of centered pentagonal numbers (A005891) which are also squares (A000290). 3
1, 3, 22, 96, 817, 3627, 31006, 137712, 1177393, 5229411, 44709910, 198579888, 1697799169, 7540806315, 64471658494, 286352060064, 2448225223585, 10873837476099, 92968086837718, 412919472031680, 3530339074609681, 15680066099727723, 134059916748330142 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 14 14:07 EDT 2021. Contains 345025 sequences. (Running on oeis4.)