A144942 Expansion of x^2*(3*x^3+145*x^2-507*x-25) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

0, 25, 532, 29237, 614312, 33739857, 708915900, 38935766125, 818088334672, 44931840368777, 944073229295972, 51851304849802917, 1089459688519217400, 59836360864832197825, 1257235536477947584012, 69051108586711506487517, 1450848719635862992732832

Offset: 1

Author

Richard Choulet, Sep 26 2008

Keywords

• easy
• nonn

Comments

Also the index of the first of two consecutive pentagonal numbers whose sum is also a pentagonal number. - Colin Barker, Dec 22 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

Crossrefs

Cf. A133301, A144796, A144797.

Programs

Mathematica

CoefficientList[Series[x (3 x^3 + 145 x^2 - 507 x - 25)/((x - 1) (x^2 - 34 x + 1) (x^2 + 34 x + 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 20 2014 *)
LinearRecurrence[{1,1154,-1154,-1,1},{0,25,532,29237,614312},20] (* Harvey P. Dale, Jun 16 2025 *)

PARI

concat(0, Vec(x^2*(3*x^3+145*x^2-507*x-25)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^20))) \\ Colin Barker, Oct 20 2014

Extensions

a(6) corrected, and more terms from Colin Barker, Oct 20 2014

Edited, name changed by Colin Barker, Oct 20 2014