A259161 -id:A259161 - cp's OEIS frontend

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

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)).

A259162 Positive hexagonal numbers (A000384) that are pentagonal numbers (A000326) divided by 2.

Original entry on oeis.org

6, 58311, 559902916, 5376187741821, 51622154137063026, 495675918647891434531, 4759480119234899417304336, 45700527609217585557064800441, 438816461344227137284036796530846, 4213515616126741362983735763224383551, 40458176507232509223142693514443734326556

Offset: 1

Colin Barker, Jun 19 2015

Intersection of A000384 and A193866 (even pentagonal numbers divided by 2). - Michel Marcus, Jun 20 2015

			6 is in the sequence because 6 is the 2nd hexagonal number, and 2*6 is the 3rd pentagonal 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. A000326, A000384, A193866, A259156-A259161, A259163-A259167.

LinearRecurrence[{9603, -9603, 1}, {6, 58311, 559902916}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Vec(-x*(x^2+693*x+6)/((x-1)*(x^2-9602*x+1)) + O(x^20))

G.f.: -x*(x^2+693*x+6) / ((x-1)*(x^2-9602*x+1)).

cp's OEIS Frontend

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

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