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A074082 Coefficient of q^2 in nu(n), where nu(0)=1, nu(1)=b and, for n>=2, nu(n)=b*nu(n-1)+lambda*(1+q+q^2+...+q^(n-2))*nu(n-2) with (b,lambda)=(1,1). 19
0, 0, 0, 0, 2, 6, 16, 37, 81, 169, 342, 675, 1307, 2491, 4686, 8718, 16066, 29364, 53282, 96065, 172215, 307151, 545286, 963993, 1697701, 2979383, 5211852, 9090060, 15810530, 27429426, 47473828, 81983773, 141286221, 243011173 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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).

REFERENCES

Paper in progress by Y. Kelly Itakura, to appear.

LINKS

Table of n, a(n) for n=0..33.

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 (3,0,-5,0,3,1).

FORMULA

G.f.: (2x^4-2x^6-x^7)/(1-x-x^2)^3.

a(n)=3a(n-1)-5a(n-3)+3a(n-5)+a(n-6) for n>=8.

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^2 are 0,0,0,0,2,6.

MATHEMATICA

b=1; lambda=1; expon=2; 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]

CROSSREFS

Coefficients of q^0, q^1 and q^3 are in A000045, A023610 and A074083. Related sequences with different values of b and lambda are in A074084-A074089.

Sequence in context: A026540 A128232 A099099 * A212383 A097813 A167821

Adjacent sequences:  A074079 A074080 A074081 * A074083 A074084 A074085

KEYWORD

nonn,easy

AUTHOR

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 19 2002

EXTENSIONS

Edited by Dean Hickerson, Aug 21 2002

STATUS

approved

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Last modified December 7 17:16 EST 2016. Contains 278890 sequences.