OFFSET
0,4
COMMENTS
The coefficient of q^0 is the Pell number A000129(n+1).
LINKS
M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002.
Index entries for linear recurrences with constant coefficients, signature (4, -2, -4, -1).
FORMULA
G.f.: (2x^3+x^4)/(1-2x-x^2)^2.
a(n) = 4a(n-1)-2a(n-2)-4a(n-3)-a(n-4) for n>=5.
EXAMPLE
The first 6 nu polynomials are nu(0)=1, nu(1)=2, nu(2)=5, nu(3)=12+2q, nu(4)=29+9q+5q^2, nu(5)=70+32q+24q^2+14q^3+2q^4, so the coefficients of q^1 are 0,0,0,2,9,32.
MATHEMATICA
b=2; lambda=1; expon=1; nu[0]=1; nu[1]=b; nu[n_] := nu[n]=Together[b*nu[n-1]+lambda(1-q^(n-1))/(1-q)nu[n-2]]; a[n_] := Coefficient[nu[n], q, expon]
(* Second program: *)
Join[{0}, LinearRecurrence[{4, -2, -4, -1}, {0, 0, 2, 9}, 30]] (* Harvey P. Dale, Apr 18 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 19 2002
EXTENSIONS
Edited by Dean Hickerson, Aug 21 2002
STATUS
approved