A253546 Centered hexagonal numbers (A003215) which are also centered heptagonal numbers (A069099).

1, 547, 368551, 248402701, 167423051797, 112842888508351, 76055939431576651, 51261590333994154297, 34550235829172628419401, 23286807687272017560521851, 15695273830985510663163308047, 10578591275276546914954509101701, 7129954824262561635168675971238301

Offset: 1

Author

Colin Barker, Jan 03 2015

Keywords

• nonn
• easy

Examples

			547 is in the sequence because it is the 14th centered hexagonal number and the 13th centered heptagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..354
• Index entries for linear recurrences with constant coefficients, signature (675,-675,1).

Crossrefs

Cf. A003215, A069099, A253457, A253458.

Programs

Mathematica

LinearRecurrence[{675,-675,1},{1,547,368551},20] (* Harvey P. Dale, Aug 03 2021 *)

PARI

Vec(-x*(x^2-128*x+1) / ((x-1)*(x^2-674*x+1)) + O(x^100))

Formula

a(n) = 675*a(n-1)-675*a(n-2)+a(n-3).

G.f.: -x*(x^2-128*x+1) / ((x-1)*(x^2-674*x+1)).