A259161 Positive pentagonal numbers (A000326) that are triangular numbers (A000217) divided by 2.

5, 48510, 465793515, 4472549283020, 42945417749765025, 412361896760694487530, 3959498889750770719498535, 38019107927025003687930446040, 365059470355795195660737423378045, 3505300996337237541709397051345542550, 33657899801770684519698434826282476187555

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..251

Index entries for linear recurrences with constant coefficients, signature (9603,-9603,1).

Formula

G.f.: -5*x*(99*x+1) / ((x-1)*(x^2-9602*x+1)).

Example

5 is in the sequence because 5 is the 2nd pentagonal number, and 2*5 is the 4th triangular number.

Mathematica

LinearRecurrence[{9603, -9603, 1}, {5, 48510, 465793515}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Prog

(PARI) Vec(-5*x*(99*x+1)/((x-1)*(x^2-9602*x+1)) + O(x^20))

Crossrefs

Cf. A000217, A000326, A074378, A259156-A259160, A259162-A259167.

Sequence in context: A355959 A165711 A167369 * A356762 A242833 A242478

Adjacent sequences: A259158 A259159 A259160 * A259162 A259163 A259164

Keyword

nonn,easy

Author

Colin Barker, Jun 19 2015

Status

approved