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Search: id:A074360
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| A074360 |
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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)=(2,2). |
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+0
6
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| 0, 0, 0, 0, 0, 40, 232, 1072, 4400, 16864, 61728, 218496, 753792, 2547840, 8468608, 27755776, 89886976, 288101888, 915089920, 2883416064, 9021001728, 28042881024, 86672025600, 266472878080, 815347462144, 2483820617728
(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 A002605.
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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: 8*x^5*(1+x)*(12*x^4+24*x^3-2*x^2-16*x+5)/(2*x^2+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)=2, nu(2)=6, nu(3)=16+4q, nu(4)=44+20q+12q^2, nu(5)=120+80q+64q^2+40q^3+8q^4, so the coefficients of q^1 are 0,0,0,0,0,40.
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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: A074360 := proc(n) RETURN( coeftayl(nu(2, 2, n), q=0, 3) ) ; end: for n from 0 to 30 do printf("%d, ", A074360(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 A002605, A074358 and A074359. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074357, A074361-A074363.
Sequence in context: A077818 A111176 A072108 this_sequence A068790 A073962 A115170
Adjacent sequences: A074357 A074358 A074359 this_sequence A074361 A074362 A074363
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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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