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

1,2

Comments

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

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).

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)).

Example

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

Prog

(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))

Crossrefs

Cf. A000217, A005891, A254626, A254627.

Cf. A000384, A254962.

Sequence in context: A281694 A250390 A284071 * A211080 A288796 A199097

Adjacent sequences: A254625 A254626 A254627 * A254629 A254630 A254631

Keyword

nonn,easy

Author

Colin Barker, Feb 03 2015

Status

approved