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Search: id:A074359
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| A074359 |
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Coefficient of q^2 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
3
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| 0, 0, 0, 0, 12, 64, 280, 1088, 3968, 13856, 46912, 155136, 503616, 1610496, 5086336, 15895552, 49229312, 151275008, 461662208, 1400356864, 4224703488, 12683452416, 37911164928, 112865394688, 334788444160, 989756825600
(list; graph; listen)
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OFFSET
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0,5
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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: 4*x^4*(-3+2*x+8*x^2+4*x^3)/(2*x^2+2*x-1)^3. [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^2 are 0,0,0,0,12,64.
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MAPLE
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nu := proc(n, b, lambda) if n = 0 then 1 ; elif n = 1 then b ; else b*nu(n-1, b, lambda)+lambda*nu(n-2, b, lambda)*add(q^i, i=0..n-2) ; fi ; end: A074359 := proc(n) local b, lambda, thisnu ; b := 2 ; lambda := 2 ; thisnu := nu(n, b, lambda) ; RETURN( coeftayl(thisnu, q=0, 2) ) ; end: for n from 0 to 40 do printf("%d, ", A074359(n) ) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 20 2007
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CROSSREFS
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Coefficient of q^0, q^1 and q^3 are in A002605, A074358 and A074360. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074357, A074361-A074363.
Sequence in context: A008425 A154507 A105916 this_sequence A104062 A003868 A001490
Adjacent sequences: A074356 A074357 A074358 this_sequence A074360 A074361 A074362
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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), Mar 20 2007
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