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

1,1

Comments

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

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).

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)).

Example

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

Mathematica

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

Prog

(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))

Crossrefs

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

Sequence in context: A036219 A022646 A268447 * A004314 A338099 A125406

Adjacent sequences: A259160 A259161 A259162 * A259164 A259165 A259166

Keyword

nonn,easy

Author

Colin Barker, Jun 19 2015

Status

approved