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%I #16 Sep 22 2017 11:48:49
%S 0,0,0,3,19,93,407,1674,6618,25455,95953,356151,1305887,4741092,
%T 17072484,61055787,217074895,767882865,2704365719,9487509102,
%U 33170122494,115614094071,401864286637,1393378817259,4820368210175
%N Coefficient of q^1 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).
%H M. Beattie, S. Dăscălescu and S. Raianu, <a href="https://arxiv.org/abs/math/0204075">Lifting of Nichols Algebras of Type B_2</a>, arXiv:math/0204075 [math.QA], 2002.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6, -7, -6, -1).
%F G.f.: (x^4+3x^3)/(1-3x-x^2)^2.
%F a(0)=0, a(1)=0, a(2)=0, a(3)=3, a(4)=19, a(n)=6*a(n-1)-7*a(n-2)- 6*a(n-3)- a(n-4). - _Harvey P. Dale_, Jan 16 2012
%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 0,0,0,3,19,93.
%t CoefficientList[Series[(x^4+3x^3)/(1-3x-x^2)^2,{x,0,30}],x] (* or *) Join[{0},LinearRecurrence[{6,-7,-6,-1},{0,0,3,19},30]] (* _Harvey P. Dale_, Jan 16 2012 *)
%Y Coefficient of q^0, q^2 and q^3 are in A006190, A074362 and A074363. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074360.
%K nonn
%O 0,4
%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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