A254333 Squares (A000290) which are also centered pentagonal numbers (A005891).

1, 16, 1156, 22801, 1666681, 32878756, 2403352576, 47411143081, 3465632747641, 68366835443776, 4997440018745476, 98584929298781641, 7206305041398228481, 142159399682007682276, 10391486872256226723856, 204993755756525779060081, 14984516863488437537571601

Offset: 1

Author

Colin Barker, Jan 28 2015

Keywords

• nonn
• easy

Examples

			16 is in the sequence because it is the 4th square number and the 3rd centered pentagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..634
• Index entries for linear recurrences with constant coefficients, signature (1,1442,-1442,-1,1).

Crossrefs

Cf. A000290, A005891, A129557, A254332.

Programs

Mathematica

LinearRecurrence[{1,1442,-1442,-1,1},{1,16,1156,22801,1666681},20] (* Harvey P. Dale, Jul 26 2015 *)

PARI

Vec(-x*(x^4+15*x^3-302*x^2+15*x+1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+1442*a(n-2)-1442*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+15*x^3-302*x^2+15*x+1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)).