OFFSET
0,6
COMMENTS
The coefficient of q^0 in nu(n) is the Fibonacci number F(n+1). The coefficient of q^1 is A023610(n-3).
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, -8, 5, 8, -2, -4, -1).
FORMULA
G.f.: (4x^5-2x^6-9x^7+x^8+6x^9+2x^10)/(1-x-x^2)^4.
a(n) = 4a(n-1)-2a(n-2)-8a(n-3)+5a(n-4)+8a(n-5)-2a(n-6)-4a(n-7)-a(n-8) for n>=11.
EXAMPLE
The first 6 nu polynomials are nu(0)=1, nu(1)=1, nu(2)=2, nu(3)=3+q, nu(4)=5+3q+2q^2, nu(5)=8+7q+6q^2+4q^3+q^4, so the coefficients of q^3 are 0,0,0,0,0,4.
MATHEMATICA
b=1; lambda=1; expon=3; 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, 0, 0}, LinearRecurrence[{4, -2, -8, 5, 8, -2, -4, -1}, {0, 0, 4, 14, 39, 97, 224, 494}, 31]] (* Jean-François Alcover, Jan 27 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 19 2002
EXTENSIONS
Edited by Dean Hickerson, Aug 21 2002
STATUS
approved