A259156 Positive triangular numbers (A000217) that are pentagonal numbers (A000326) divided by 2.

6, 105, 58311, 1008910, 559902916, 9687554415, 5376187741821, 93019896484620, 51622154137063026, 893177036357767525, 495675918647891434531, 8576285810087387291130, 4759480119234899417304336, 82349495455282056411663435, 45700527609217585557064800441

Offset: 1

Author

Colin Barker, Jun 19 2015

Keywords

• nonn
• easy

Comments

Intersection of A000217 and A193866 (even pentagonal numbers divided by 2). - Michel Marcus, Jun 20 2015

Examples

			6 is in the sequence because 6 is the 3rd triangular number, and 2*6 is the 3rd pentagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..502
• Index entries for linear recurrences with constant coefficients, signature (1,9602,-9602,-1,1).

Crossrefs

Cf. A000217, A000326, A193866, A259157-A259167.

Programs

Mathematica

LinearRecurrence[{1, 9602, -9602, -1, 1}, {6, 105, 58311, 1008910, 559902916}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

PARI

Vec(-x*(x^3+594*x^2+99*x+6)/((x-1)*(x^2-98*x+1)*(x^2+98*x+1)) + O(x^20))

Formula

G.f.: -x*(x^3+594*x^2+99*x+6) / ((x-1)*(x^2-98*x+1)*(x^2+98*x+1)).