%I A072946
%S A072946 1,2,6,4,12,8,24,16,48,32,96,64,192,128,384,256,768,512,1536,1024,3072,
%T A072946 2048,6144,4096,12288,8192,24576,16384,49152,32768,98304,65536,196608,
%U A072946 131072,393216,262144,786432,524288,1572864,1048576,3145728,2097152
%N A072946 Coefficient of the highest power of q in the expansion of nu(0)=1, nu(1)=b 
               and for n>=2, nu(n)=b*nu(n-1)+lambda*(n-1)_q*nu(n-2) with (b,lambda)=(2,
               2), where (n)_q=(1+q+...+q^(n-1)) and q is a root of unity.
%C A072946 Instead of listing the coefficients of the highest power of q in each 
               nu(n), if we listed the coefficients of the smallest power of q (i.e. 
               constant terms), we get a weighted Fibonacci numbers described by 
               f(0)=1, f(1)=1, for n>=2, f(n)=2f(n-1)+2f(n-2).
%H A072946 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 A072946 for given b and lambda, the recurrence relation is given by; t(0)=1, 
               t(1)=b, t(2)=b^2+lambda and for n>=3, t(n)=lambda*T(n-2)
%F A072946 O.g.f.: -(1+2*x+4*x^2)/(-1+2*x^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Dec 05 2007
%e A072946 nu(0)=1, nu(1)=2, nu(2)=6, nu(3)=16+4q, nu(4)=44+20q+12q^2, nu(5)=120+80q+64q^2+40q^3+8q^4, 
               nu(6)=328+288q+280q^2+232q^3+168q^4+64q^5+24q^6. By listing the coefficients 
               of the highest power in each nu(n) we get 1,2,6,4,12,8,24,...
%Y A072946 Cf. A002605.
%Y A072946 Sequence in context: A059909 A145177 A007517 this_sequence A134000 A127730 
               A118416
%Y A072946 Adjacent sequences: A072943 A072944 A072945 this_sequence A072947 A072948 
               A072949
%K A072946 nonn
%O A072946 0,2
%A A072946 Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002
%E A072946 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007