A253411 Indices of centered octagonal numbers (A016754) which are also centered pentagonal numbers (A005891).

1, 76, 646, 108871, 930811, 156991186, 1342228096, 226381180621, 1935491982901, 326441505463576, 2790978097114426, 470728424497295251, 4024588480547018671, 678790061683594287646, 5803453797970703808436, 978814798219318465489561, 8368576352085274344745321

Offset: 1

Author

Colin Barker, Dec 31 2014

Keywords

• nonn
• easy

Comments

Also positive integers y in the solutions to 5*x^2 - 8*y^2 - 5*x + 8*y = 0, the corresponding values of x being A253410.

Examples

			76 is in the sequence because the 76th centered octagonal number is 22801, which is also the 96th centered pentagonal 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, A253410, A253579.

Programs

Mathematica

LinearRecurrence[{1,1442,-1442,-1,1},{1,76,646,108871,930811},20] (* Harvey P. Dale, Feb 04 2016 *)

PARI

Vec(-x*(x^4+75*x^3-872*x^2+75*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*(x^4 + 75*x^3 - 872*x^2 + 75*x + 1) / ((x-1)*(x^2 - 38*x + 1)*(x^2 + 38*x + 1)).