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

1,1

Comments

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

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).

Formula

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

Example

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

Mathematica

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

Prog

(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))

Crossrefs

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

Sequence in context: A109819 A162130 A048707 * A075068 A055763 A213464

Adjacent sequences: A259153 A259154 A259155 * A259157 A259158 A259159

Keyword

nonn,easy

Author

Colin Barker, Jun 19 2015

Status

approved