A253410 Indices of centered pentagonal numbers (A005891) which are also centered octagonal numbers (A016754).

1, 96, 817, 137712, 1177393, 198579888, 1697799169, 286352060064, 2448225223585, 412919472031680, 3530339074609681, 595429592317621776, 5090746497361935697, 858609059202538568592, 7340852918856836664673, 1238113667940468298287168, 10585504818245061108522049

Offset

1,2

Comments

Also positive integers x in the solutions to 5*x^2 - 8*y^2 - 5*x + 8*y = 0, the corresponding values of y being A253411.

Links

Colin Barker, Table of n, a(n) for n = 1..633

Index entries for linear recurrences with constant coefficients, signature (1,1442,-1442,-1,1).

Formula

a(n) = a(n-1) + 1442*a(n-2) - 1442*a(n-3) - a(n-4) + a(n-5).

G.f.: x*(95*x^3 + 721*x^2 - 95*x - 1) / ((x-1)*(x^2 - 38*x + 1)*(x^2 + 38*x + 1)).

Example

96 is in the sequence because the 96th centered pentagonal number is 22801, which is also the 76th centered octagonal number.

Mathematica

LinearRecurrence[{1, 1442, -1442, -1, 1}, {1, 96, 817, 137712, 1177393}, 20] (* Harvey P. Dale, Jul 12 2021 *)

Prog

(PARI) Vec(x*(95*x^3+721*x^2-95*x-1)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

Crossrefs

Cf. A005891, A016754, A253411, A253579.

Sequence in context: A187610 A269215 A096783 * A326576 A202890 A173615

Adjacent sequences: A253407 A253408 A253409 * A253411 A253412 A253413

Keyword

nonn,easy

Author

Colin Barker, Dec 31 2014

Status

approved