OFFSET
0,2
LINKS
M. R. Bremner, Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures, arXiv preprint arXiv:1303.0920, 2013
N. J. A. Sloane, Transforms
Index entries for linear recurrences with constant coefficients, signature (4,0,-4,1).
FORMULA
a(n) = (1/12)*((7-4*sqrt(3))*(2-sqrt(3))^n+(7+4*sqrt(3))*(2+sqrt(3))^n-3+(-1)^n). Recurrence: a(n) = 4*a(n-1)-4*a(n-3)+a(n-4).
a(n)=sum{k=0..floor(n/2), U(n-2k, 2)} - Paul Barry, Nov 15 2003
The g.f. can also be written as 1/(1-4*x+4*x^3-x^4), which relates this sequence to the family of sequences described in A225682.
MATHEMATICA
CoefficientList[Series[1/((1-x^2)*(1-4x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, 0, -4, 1}, {1, 4, 16, 60}, 30] (* Harvey P. Dale, Aug 22 2015 *)
PROG
(PARI) Vec(1/((1-x^2)*(1-4*x+x^2))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 15 2002
STATUS
approved