OFFSET
0,4
COMMENTS
Binomial transform is A128213.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-2,-3,-2,-1).
FORMULA
G.f.: (1+2x+3x^2)/(1+x+x^2)^2.
a(n) = (1-n)*cos(2*Pi*n/3)+(n-1)*sin(2*Pi*n/3)/sqrt(3).
From Wesley Ivan Hurt, Mar 15 2015: (Start)
a(n) + 2*a(n-1) + 3*a(n-2) + 2*a(n-3) + a(n-4) = 0.
a(n) = (n-1) * ((n-2)^2 mod 3) * (-1)^floor((2n-2)/3). (End)
MATHEMATICA
CoefficientList[Series[(1 + 2 x + 3 x^2)/(1 + x + x^2)^2, {x, 0, 50}], x] (* Wesley Ivan Hurt, Mar 15 2015 *)
LinearRecurrence[{-2, -3, -2, -1}, {1, 0, 0, -2}, 70] (* Harvey P. Dale, Jul 16 2021 *)
PROG
(PARI) Vec((1+2*x+3*x^2)/(1+x+x^2)^2 + O(x^80)) \\ Michel Marcus, Mar 16 2015
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Feb 19 2007
EXTENSIONS
More terms from Wesley Ivan Hurt, Mar 15 2015
STATUS
approved