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 A074354 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)=(1,2). 5
 0, 0, 0, 0, 0, 14, 64, 218, 692, 1982, 5496, 14562, 37692, 95142, 236032, 576074, 1387780, 3304078, 7787656, 18190386, 42151116, 96972534, 221651472, 503650970, 1138286740, 2559944414, 5731095704, 12776843138, 28374100572 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Coefficient of q^0 is A001045(n+1). LINKS M. Beattie, S. Dăscălescu and S. Raianu, Lifting of Nichols Algebras of Type B_2, arXiv:math/0204075 [math.QA], 2002. FORMULA Conjectures from Colin Barker, Nov 18 2017: (Start) G.f.: 2*x^5*(1 + 2*x)*(7 - 10*x - 13*x^2 + 12*x^3 + 12*x^4) / ((1 + x)^4*(1 - 2*x)^4). a(n) = 4*a(n-1) + 2*a(n-2) - 20*a(n-3) - a(n-4) + 40*a(n-5) + 8*a(n-6) - 32*a(n-7) - 16*a(n-8) for n>10. (End) EXAMPLE The first 6 nu polynomials are nu(0)=1, nu(1)=1, nu(2)=3, nu(3)=5+2q, nu(4)=11+8q+6q^2, nu(5)=21+22q+20q^2+14q^3+4q^4, so the coefficients of q^1 are 0,0,0,0,0,14. CROSSREFS Coefficients of q^0, q^1 and q^2 are in A001045, A074352 and A074353. Related sequences with other values of b and lambda are in A074082-A074089, A074035-A074363. Sequence in context: A050396 A069964 A275127 * A212743 A124892 A126401 Adjacent sequences:  A074351 A074352 A074353 * A074355 A074356 A074357 KEYWORD nonn AUTHOR Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002 EXTENSIONS More terms from Benoit Cloitre, Jan 16 2003 Corrected by T. D. Noe, Oct 25 2006 STATUS approved

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Last modified April 16 07:59 EDT 2021. Contains 343030 sequences. (Running on oeis4.)