A107736 Pentagonal numbers that are half other pentagonal numbers.

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

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..163

Index entries for linear recurrences with constant coefficients, signature (1331715,-1331715,1).

Formula

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

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

Example

a(2)=((A001653(6)^2-1)/24=(33461^2-1)/24=46651605.

Mathematica

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

Prog

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

Crossrefs

Cf. A001653, A000326.

Sequence in context: A110596 A286178 A126029 * A261121 A139474 A240129

Adjacent sequences: A107733 A107734 A107735 * A107737 A107738 A107739

Keyword

nonn,easy

Author

Franz Vrabec, Aug 26 2006

Status

approved