OFFSET
1,1
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Harvey P. Dale, Mar 04 2014: (Start)
G.f.: -9*x*(3*x^2-8*x+7)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), a(1)=63, a(2)=117, a(3)=189. (End)
From Elmo R. Oliveira, Sep 12 2025: (Start)
E.g.f.: 9*(-3 + (3 + 4*x + x^2)*exp(x)).
a(n) = 9*(n^2 + 3*n + 3).
a(n) = 9*A002061(n+2). (End)
MATHEMATICA
Table[(n+3)^3-n^3, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {63, 117, 189}, 50] (* Harvey P. Dale, Mar 04 2014 *)
PROG
(PARI) a(n)=(n+3)^3-n^3 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved