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Search: id:A074356
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| A074356 |
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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)=(1,3). |
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+0
3
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| 0, 0, 0, 0, 12, 42, 180, 561, 1833, 5373, 15798, 44367, 123561, 336243, 906054, 2408094, 6344832, 16561824, 42922602, 110472933, 282678423, 719404803, 1822117962, 4594816221, 11540742615, 28880919975, 72033463644, 179107709004
(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 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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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^2 are 0,0,0,0,12,42.
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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: A074356 := proc(n) local b, lambda, thisnu ; b := 1 ; lambda := 3 ; thisnu := nu(n, b, lambda) ; RETURN( coeftayl(thisnu, q=0, 2) ) ; end: for n from 0 to 40 do printf("%d, ", A074356(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 A006130, A074355 and A074357. Related sequences with other values of b and lambda are in A074082-A074089, A074352-A074354, A074358-A074363.
Sequence in context: A009948 A007586 A122973 this_sequence A088826 A125221 A082829
Adjacent sequences: A074353 A074354 A074355 this_sequence A074357 A074358 A074359
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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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