OFFSET
0,4
COMMENTS
The coefficient of q^0 is A014983(n+1).
LINKS
G. C. Greubel, 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 (4,2,-12,-9).
FORMULA
G.f.: (6*x^3 +9*x^4)/(1-2*x-3*x^2)^2.
a(n) = 4*a(n-1) +2*a(n-2) -12*a(n-3) -9*a(n-4) for n>=5.
EXAMPLE
The first 6 nu polynomials are nu(0)=1, nu(1)=2, nu(2)=7, nu(3)=20+6q, nu(4)=61+33q+21q^2, nu(5)=182+144q+120q^2+78q^3+18q^4, so the coefficients of q^1 are 0,0,0,6,33,144.
MATHEMATICA
b=2; lambda=3; 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, -12, -9}, {0, 0, 6, 33}, 50]] (* G. C. Greubel, May 26 2018 *)
PROG
(PARI) x='x+O('x^30); concat([0, 0, 0], Vec((6*x^3 +9*x^4)/(1-2*x-3*x^2)^2)) \\ G. C. Greubel, May 26 2018
(Magma) I:=[0, 0, 6, 33]; [0] cat [n le 4 select I[n] else 4*Self(n-1) + 2*Self(n-2) -12*Self(n-3) -9*Self(n-4): n in [1..30]]; // G. C. Greubel, May 26 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 19 2002
EXTENSIONS
Edited by Dean Hickerson, Aug 21 2002
STATUS
approved