A254137 Indices of centered hexagonal numbers (A003215) which are also pentagonal numbers (A000326).

1, 52, 629, 59432, 725289, 68583900, 836982301, 79145760592, 965876849489, 91334139138692, 1114621047327429, 105399517420289400, 1286271722739003001, 121630951768874828332, 1484356453419762135149, 140362012941764131605152, 1712946060974682764958369

Offset: 1

Author

Colin Barker, Jan 26 2015

Keywords

• nonn
• easy

Comments

Also positive integers y in the solutions to 3*x^2 - 6*y^2 - x + 6*y - 2 = 0, the corresponding values of x being A254136.

Examples

			52 is in the sequence because the 52nd centered hexagonal number is 7957, which is also the 73rd pentagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..653
• Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

Crossrefs

Cf. A000326, A003215, A254136, A254138.

Programs

PARI

Vec(x*(51*x^3+577*x^2-51*x-1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(51*x^3+577*x^2-51*x-1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).