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

Author

Colin Barker, Jun 19 2015

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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