A107736 Pentagonal numbers that are half other pentagonal numbers.

35, 46651605, 62126595542551, 82734857056306152425, 110179167429819564875005515, 146727139774551997160896788291901, 195398586217617559179696685958485684415, 260215032846061623065656040447357907946787025, 346532002251364709713039450689133092337489050568051

Offset: 1

Author

Franz Vrabec, Aug 26 2006

Keywords

• nonn
• easy

Examples

			a(2) = (A001653(7)^2-1)/24 = (33461^2-1)/24 = 46651605.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..163
• Index entries for linear recurrences with constant coefficients, signature (1331715,-1331715,1).

Crossrefs

Cf. A001653, A000326.

Programs

Mathematica

LinearRecurrence[{1331715,-1331715,1},{35,46651605,62126595542551},20] (* Harvey P. Dale, Aug 04 2020 *)

PARI

Vec(-x*(x^2+41580*x+35)/((x-1)*(x^2-1331714*x+1)) + O(x^20)) \\ Colin Barker, Jun 18 2015

Formula

a(n) = (A001653(4*n-1)^2-1)/24.

G.f.: -x*(x^2+41580*x+35) / ((x-1)*(x^2-1331714*x+1)). - Colin Barker, Jun 18 2015