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

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..354

Index entries for linear recurrences with constant coefficients, signature (675,-675,1).

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)).

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A003215, A069099, A253457, A253458.

Sequence in context: A123099 A263524 A300899 * A015324 A103537 A136928

Adjacent sequences: A253543 A253544 A253545 * A253547 A253548 A253549

Keyword

nonn,easy

Author

Colin Barker, Jan 03 2015

Status

approved