OFFSET
0,4
COMMENTS
Coefficient of q^0 is A001045(n+1).
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
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 (2,3,-4,-4).
FORMULA
a(0) = 0 for n>0, a(n) = (1/27)*(2^n*(6*n-11) + (-1)^n*(6*n-16)).
From Colin Barker, Nov 18 2017: (Start)
G.f.: 2*x^3*(1 + 2*x) / ((1 + x)^2*(1 - 2*x)^2).
a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4) for n>4.
(End)
EXAMPLE
The first 6 nu polynomials are nu(0)=1, nu(1)=1, nu(2)=3, nu(3)=5+2q, nu(4)=11+8q+6q^2, nu(5)=21+22q+20q^2+14q^3+4q^4, so the coefficients of q^1 are 0,0,0,2,8,22.
PROG
(PARI) a(n)=if(n<1, 0, (1/27)*(2^n*(6*n-11)+(-1)^n*(6*n-16)))
(PARI) a(n)=if(n<1, 0, (1/81)*(2^(n-1)*(6*n^2-43)+ (-1)^n*(6*n^2-24*n+62)))
(PARI) concat(vector(3), Vec(2*x^3*(1 + 2*x) / ((1 + x)^2*(1 - 2*x)^2) + O(x^40))) \\ Colin Barker, Nov 18 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002
EXTENSIONS
More terms and formula from Benoit Cloitre, Jan 12 2003
Corrected by Franklin T. Adams-Watters, Oct 25 2006
Corrected by T. D. Noe, Oct 25 2006
STATUS
approved