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Search: id:A074357
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| A074357 |
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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). |
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+0
6
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| 0, 0, 0, 0, 0, 30, 168, 639, 2415, 7872, 25542, 77727, 233547, 679410, 1949862, 5490132, 15276456, 41963844, 114153990, 307595853, 822263313, 2181777252, 5751280350, 15069310365, 39269077809, 101817186264, 262776963360
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Coefficient of q^0 is A006130.
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REFERENCES
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Paper in progress by Y. Kelly Itakura, to appear.
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LINKS
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M. Beattie, S. D\u{a}sc\u{a}lescu and S. Raianu, Lifting of Nichols Algebras of Type $B_2$
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FORMULA
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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]
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EXAMPLE
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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.
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MAPLE
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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
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CROSSREFS
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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.
Sequence in context: A064240 A141221 A159884 this_sequence A140594 A100430 A159653
Adjacent sequences: A074354 A074355 A074356 this_sequence A074358 A074359 A074360
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KEYWORD
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nonn
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AUTHOR
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Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 20 2006
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