%I A074357
%S A074357 0,0,0,0,0,30,168,639,2415,7872,25542,77727,233547,679410,1949862,
%T A074357 5490132,15276456,41963844,114153990,307595853,822263313,2181777252,
%U A074357 5751280350,15069310365,39269077809,101817186264,262776963360
%N A074357 Coefficient of q^3 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)=(1,3).
%C A074357 Coefficient of q^0 is A006130.
%D A074357 Paper in progress by Y. Kelly Itakura, to appear.
%H A074357 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 A074357 Conjecture: O.g.f.: 3*x^5*(3*x+1)*(36*x^4+24*x^3-29*x^2-14*x+10)/(3*x^2+x-1)^4. 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 22 2009]
%e A074357 The first 6 nu polynomials are nu(0)=1, nu(1)=1, nu(2)=4, nu(3)=7+3q, 
               nu(4)=19+15q+12q^2, nu(5)=40+45q+42q^2+30q^3+9q^4, so the coefficients 
               of q^3 are 0,0,0,0,0,30.
%p A074357 nu := proc(b,lambda,n) global q; local qp,i ; if n = 0 then RETURN(1) 
               ; elif n =1 then RETURN(b) ; fi ; qp:=0 ; for i from 0 to n-2 do 
               qp := qp + q^i ; od ; RETURN( b*nu(b,lambda,n-1)+lambda*qp*nu(b,lambda,
               n-2)) ; end: A074357 := proc(n) RETURN( coeftayl(nu(1,3,n),q=0,3) 
               ) ; end: for n from 0 to 30 do printf("%d,", A074357(n)) ; od ; - 
               R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 20 2006
%Y A074357 Coefficient of q^0, q^1 and q^2 are in A006130, A074355 and A074356. 
               Related sequences with other values of b and lambda are in A074082-A074089, 
               A074352-A074354, A074358-A074363.
%Y A074357 Sequence in context: A064240 A141221 A159884 this_sequence A140594 A100430 
               A159653
%Y A074357 Adjacent sequences: A074354 A074355 A074356 this_sequence A074358 A074359 
               A074360
%K A074357 nonn
%O A074357 0,6
%A A074357 Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002
%E A074357 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 20 2006