A259159 -id:A259159 - cp's OEIS frontend

A259158 Positive triangular numbers (A000217) that are heptagonal numbers (A000566) divided by 2.

171, 355817826, 739874066553765, 1538466018777014327028, 3199027777735470191011289295, 6651936797966044301302839516949686, 13831784604089070782667939513452521937961, 28761287297921206463992005998270360082445758120

Offset: 1

Colin Barker, Jun 19 2015

			171 is in the sequence because 171 is the 18th triangular number, and 2*171 is the 12th heptagonal number.

Colin Barker, Table of n, a(n) for n = 1..158
Index entries for linear recurrences with constant coefficients, signature (2079363,-2079363,1).

Cf. A000217, A000566, A259156, A259157, A259159-A259167.

LinearRecurrence[{2079363, -2079363, 1}, {171, 355817826, 739874066553765}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Vec(-171*x*(1443*x+1) / ((x-1)*(x^2-2079362*x+1)) + O(x^20))

G.f.: -171*x*(1443*x+1) / ((x-1)*(x^2-2079362*x+1)).

A259160 Positive squares (A000290) that are octagonal numbers (A000567) divided by 2.

Original entry on oeis.org

4, 39204, 376437604, 3614553835204, 34706945549192004, 333256087548787788004, 3199924917936514791223204, 30725678728770327476537417604, 295027963953727766493197492611204, 2832858479158015285097354847515364004, 27201106821847298813777034752645032556004

Offset: 1

Colin Barker, Jun 19 2015

Intersection of A000290 and A033579 (even octagonal numbers divided by 2). - Michel Marcus, Jun 20 2015

			4 is in the sequence because 4 is the 2nd square, and 2*4 is the 2nd octagonal number.

Colin Barker, Table of n, a(n) for n = 1..251
Index entries for linear recurrences with constant coefficients, signature (9603,-9603,1).

Cf. A000290, A000567, A033579, A259156-A259159, A259161-A259167.

LinearRecurrence[{9603, -9603, 1}, {4, 39204, 376437604}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Vec(-4*x*(x^2+198*x+1)/((x-1)*(x^2-9602*x+1)) + O(x^20))

G.f.: -4*x*(x^2+198*x+1) / ((x-1)*(x^2-9602*x+1)).

cp's OEIS Frontend

A259158 Positive triangular numbers (A000217) that are heptagonal numbers (A000566) divided by 2.

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