OFFSET
1,1
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(32821201 + 32788798*x + x^2)/(1-x)^3.
E.g.f.: -1 + (1 + 32821200*x + 32805000*x^2)*exp(x). - G. C. Greubel, Jan 27 2022
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {32821201, 131252401, 295293601}, 40]
PROG
(Magma) I:=[32821201, 131252401, 295293601]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n)=32805000*n^2+16200*n+1 \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [16200*n*(2025*n + 1) + 1 for n in (1..30)] # G. C. Greubel, Jan 27 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 22 2009
STATUS
approved