A254628 Triangular numbers (A000217) that are also centered pentagonal numbers (A005891).

1, 6, 276, 1891, 88831, 608856, 28603266, 196049701, 9210162781, 63127394826, 2965643812176, 20326825084231, 954928097357851, 6545174549727516, 307483881705415806, 2107525878187175881, 99008854981046531641, 678616787601720906126, 31880543820015277772556

Offset: 1

Author

Colin Barker, Feb 03 2015

Keywords

• nonn
• easy

Comments

Also hexagonal numbers (A000384) that are also centered pentagonal numbers (A005891). - Colin Barker, Feb 11 2015

Examples

			6 is in the sequence because it is the 3rd triangular number and the 2nd centered pentagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..798
• Index entries for linear recurrences with constant coefficients, signature (1,322,-322,-1,1).

Crossrefs

Cf. A000217, A005891, A254626, A254627.

Cf. A000384, A254962.

Programs

PARI

Vec(-x*(x^4+5*x^3-52*x^2+5*x+1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+322*a(n-2)-322*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+5*x^3-52*x^2+5*x+1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)).