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A253716
Hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099).
3
1, 16322041, 4145734153, 67933251842771953, 17254778510170993681, 282742011610770921096804841, 71815357774355276244995175961, 1176788140728629029198108610250463201, 298899554649081431834808455098428958753, 4897858370145334123819452782766901335994312153
OFFSET
1,2
FORMULA
a(n) = 4162056194*a(n-2)-a(n-4).
G.f.: -x*(x-1)*(x^2+16322042*x+1) / ((x^2-64514*x+1)*(x^2+64514*x+1)).
EXAMPLE
16322041 is in the sequence because it is the 2857th hexagonal number and the 2160th centered heptagonal number.
MATHEMATICA
LinearRecurrence[{0, 4162056194, 0, -1}, {1, 16322041, 4145734153, 67933251842771953}, 20] (* Harvey P. Dale, Jan 05 2017 *)
PROG
(PARI) Vec(-x*(x-1)*(x^2+16322042*x+1)/((x^2-64514*x+1)*(x^2+64514*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 10 2015
STATUS
approved