OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
R. Choulet, Curtz-like transformation.
Index entries for linear recurrences with constant coefficients, signature (3,-2,1).
FORMULA
O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4+z^6) + (z/(1-3*z+2*z^2-z^3)) + ((1-z+z^2)/(1-3*z+2*z^2-z^3)).
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 9, with a(0)=2, a(1)=4, a(2)=9, a(3)=23, a(4)=55, a(5)=126, a(6)=293, a(7)=680, a(8)=1581.
MATHEMATICA
Join[{2, 4, 9, 23, 55, 126}, LinearRecurrence[{3, -2, 1}, {293, 680, 1581}, 45]] (* G. C. Greubel, Jun 26 2018 *)
PROG
(PARI) z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4+z^6) + (z/(1-3*z+2*z^2-z^3)) + ((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 26 2018
(Magma) I:=[293, 680, 1581]; [2, 4, 9, 23, 55, 126] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 26 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Apr 10 2009
STATUS
approved