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

1,2

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.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (9,-9,1).

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

Example

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

Prog

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

Crossrefs

Cf. A005448, A005891, A182432, A253654.

Sequence in context: A285392 A327091 A201351 * A188899 A052203 A371775

Adjacent sequences: A253467 A253468 A253469 * A253471 A253472 A253473

Keyword

nonn,easy

Author

Colin Barker, Jan 01 2015

Status

approved