A259157 Positive triangular numbers (A000217) that are hexagonal numbers (A000384) divided by 2.

3, 3570, 4119885, 4754343828, 5486508657735, 6331426236682470, 7306460390622912753, 8431648959352604634600, 9730115592632515125415755, 11228544962248963102125146778, 12957731156319710787337293966165, 14953210525847983999624135111807740

Offset: 1

Author

Colin Barker, Jun 19 2015

Keywords

• nonn
• easy

Comments

Intersection of A000217 and A033991 (even hexagonal numbers divided by 2). - Michel Marcus, Jun 20 2015

Examples

			3 is in the sequence because 3 is the 2nd triangular number, and 2*3 is the 2nd hexagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..327
• Index entries for linear recurrences with constant coefficients, signature (1155,-1155,1).

Crossrefs

Cf. A000217, A000384, A033991, A259156, A259158-A259167.

Programs

Mathematica

LinearRecurrence[{1155, -1155, 1}, {3, 3570, 4119885}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

PARI

Vec(-3*x*(35*x+1)/((x-1)*(x^2-1154*x+1)) + O(x^20))

Formula

G.f.: -3*x*(35*x+1) / ((x-1)*(x^2-1154*x+1)).

a(n) = 1155*a(n-1) - 1155*a(n-2) + a(n-3). - Wesley Ivan Hurt, Aug 04 2025