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Search: id:A074352
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| A074352 |
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Coefficient of q^1 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). |
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+0
12
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| 0, 0, 0, 2, 8, 22, 60, 146, 352, 814, 1860, 4170, 9256, 20326, 44300, 95874, 206320, 441758, 941780, 2000058, 4233144, 8932310, 18796700, 39457522, 82643328, 172743182, 360399460, 750625066, 1560902472, 3241109574, 6720828460
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Coefficient of q^0 is A001045(n+1).
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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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a(0)=0 for n>0, a(n)=(1/27)*(2^n*(6*n-11)+(-1)^n*(6*n-16)).
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EXAMPLE
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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 0,0,0,2,8,22.
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PROGRAM
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(PARI) a(n)=if(n<1, 0, (1/27)*(2^n*(6*n-11)+(-1)^n*(6*n-16)))
(PARI) a(n)=if(n<1, 0, (1/81)*(2^(n-1)*(6*n^2-43)+ (-1)^n*(6*n^2-24*n+62)))
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CROSSREFS
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Coefficient of q^0, q^2 and q^3 are in A001045, A074353 and A074354. Related sequences with other values of b and lambda are in A074082-A074089, A074035-A074363.
Sequence in context: A006732 A005803 A145654 this_sequence A017928 A102880 A137104
Adjacent sequences: A074349 A074350 A074351 this_sequence A074353 A074354 A074355
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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 and formula from Ben Cloitre, Jan 12, 2003
Corrected by Franklin T. Adams-Watters, Oct 25 2006
Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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