A253470 Indices of centered triangular numbers (A005448) which are also centered pentagonal numbers (A005891).

1, 5, 36, 280, 2201, 17325, 136396, 1073840, 8454321, 66560725, 524031476, 4125691080, 32481497161, 255726286205, 2013328792476, 15850904053600, 124793903636321, 982500325036965, 7735208696659396, 60899169248238200, 479458145289246201, 3774765993065731405

Offset: 1

Author

Colin Barker, Jan 01 2015

Keywords

• nonn
• easy

Comments

Also indices of pentagonal numbers (A000326) which are also centered pentagonal numbers (A005891).

Also positive integers x in the solutions to 3*x^2 - 5*y^2 - 3*x + 5*y = 0, the corresponding values of y being A182432.

Examples

			5 is in the sequence because the 5th centered triangular number is 31, which is also the 4th centered pentagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-9,1).

Crossrefs

Cf. A005448, A005891, A182432, A253654.

Programs

PARI

Vec(x*(4*x-1)/((x-1)*(x^2-8*x+1)) + O(x^100))

Formula

a(n) = 9*a(n-1)-9*a(n-2)+a(n-3).

G.f.: x*(4*x-1) / ((x-1)*(x^2-8*x+1)).

a(n) = (6-(4-sqrt(15))^n*(3+sqrt(15))+(-3+sqrt(15))*(4+sqrt(15))^n)/12. - Colin Barker, Mar 03 2016