A259163 Positive heptagonal numbers (A000566) that are triangular numbers (A000217) divided by 2.

18, 189, 37727235, 393298308, 78448579122960, 817809556618215, 163122994382238923193, 1700522115268371779430, 339191755844562643229618814, 3536001066647854270462804353, 705302447816298343956844397692383, 7352626249945315029422809413582264

Offset: 1

Author

Colin Barker, Jun 19 2015

Keywords

• nonn
• easy

Comments

Intersection of A000566 and A074378 (even triangular numbers divided by 2). - Michel Marcus, Jun 20 2015

Examples

			18 is in the sequence because 18 is the 3rd heptagonal number, and 2*18 is the 8th triangular number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..317
• Index entries for linear recurrences with constant coefficients, signature (1,2079362,-2079362,-1,1).

Crossrefs

Cf. A000217, A000566, A074378, A259156-A259162, A259164-A259167.

Programs

Mathematica

LinearRecurrence[{1, 2079362, -2079362, -1, 1}, {18, 189, 37727235, 393298308, 78448579122960}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

PARI

Vec(-9*x*(2*x^4+19*x^3+33170*x^2+19*x+2)/((x-1)*(x^2-1442*x+1)*(x^2+1442*x+1)) + O(x^20))

Formula

G.f.: -9*x*(2*x^4+19*x^3+33170*x^2+19*x+2) / ((x-1)*(x^2-1442*x+1)*(x^2+1442*x+1)).