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A253546
Centered hexagonal numbers (A003215) which are also centered heptagonal numbers (A069099).
3
1, 547, 368551, 248402701, 167423051797, 112842888508351, 76055939431576651, 51261590333994154297, 34550235829172628419401, 23286807687272017560521851, 15695273830985510663163308047, 10578591275276546914954509101701, 7129954824262561635168675971238301
OFFSET
1,2
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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 03 2015
STATUS
approved