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

Author

Colin Barker, Dec 31 2014

Keywords

• nonn
• easy

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.

Examples

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

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).

Crossrefs

Cf. A005891, A016754, A253411, A253579.

Programs

Mathematica

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

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))

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)).