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

1,2

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.

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).

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)).

Example

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

Prog

(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))

Crossrefs

Cf. A000326, A003215, A254136, A254138.

Sequence in context: A285753 A100413 A221272 * A249712 A255945 A215365

Adjacent sequences: A254134 A254135 A254136 * A254138 A254139 A254140

Keyword

nonn,easy

Author

Colin Barker, Jan 26 2015

Status

approved