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 A074362 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)=(3,1). 2

%I

%S 0,0,0,0,10,66,336,1527,6513,26667,106102,413265,1583331,5986689,

%T 22392606,83002842,305308666,1115587020,4052786850,14648359515,

%U 52705460583,188868467853,674332868566,2399653030899,8513523719661

%N 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)=(3,1).

%C Coefficient of q^0 is A006190(n+1).

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

%H M. Beattie, S. D\u{a}sc\u{a}lescu and S. Raianu, <a href="http://front.math.ucdavis.edu/math.QA/0204075">Lifting of Nichols Algebras of Type \$B_2\$</a>

%F G.f.: (-3x^7-18x^6-24x^5+10x^4)/(1-3x-x^2)^3.

%e The first 6 nu polynomials are nu(0)=1, nu(1)=3, nu(2)=10, nu(3)=33+3q, nu(4)=109+19q+10q^2, nu(5)=360+93q+66q^2+36q^3+3q^4, so the coefficients of q^1 are 0,0,0,0,10,66.

%Y Coefficient of q^0, q^1 and q^3 are in A006190, A074361 and A074363. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074360.

%K nonn

%O 0,5

%A Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002

%E More terms from Brent Lehman (mailbjl(AT)yahoo.com), Aug 25 2002

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