This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A074357 #20 Sep 22 2017 11:41:23
%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.
%H A074357 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 A074357 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,6,-32,-19,96,54,-108,-81).
%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. - _R. J. Mathar_, 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_, Sep 20 2006
%t A074357 Join[{0, 0, 0}, LinearRecurrence[{4, 6, -32, -19, 96, 54, -108, -81}, {0, 0, 30, 168, 639, 2415, 7872, 25542}, 24]] (* _Jean-François Alcover_, Sep 22 2017 *)
%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.
%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_, Sep 20 2006