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Search: id:A074089
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| A074089 |
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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)=(2,3). |
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+0
20
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| 0, 0, 0, 0, 0, 78, 501, 2574, 11757, 50034, 203229, 797316, 3046362, 11394774, 41885913, 151732722, 542840175, 1921208586, 6735519249, 23417342568, 80810560596, 277008392478, 943826398893, 3198199361910, 10783017814065
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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The coefficient of q^0 is A014983(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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G.f.: (78x^5-123x^6-498x^7+297x^8+1134x^9+567x^10)/(1-2x-3x^2)^4.
a(n)=8a(n-1)-12a(n-2)-40a(n-3)+74a(n-4)+120a(n-5)-108a(n-6)-216a(n-7)-81a(n-8) for n>=11.
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EXAMPLE
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The first 6 nu polynomials are nu(0)=1, nu(1)=2, nu(2)=7, nu(3)=20+6q, nu(4)=61+33q+21q^2, nu(5)=182+144q+120q^2+78q^3+18q^4, so the coefficients of q^3 are 0,0,0,0,0,78.
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MATHEMATICA
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b=2; lambda=3; expon=3; nu[0]=1; nu[1]=b; nu[n_] := nu[n]=Together[b*nu[n-1]+lambda(1-q^(n-1))/(1-q)nu[n-2]]; a[n_] := Coefficient[nu[n], q, expon]
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CROSSREFS
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Coefficients of q^0, q^1 and q^2 are in A014983, A074087 and A074088. Related sequences with other values of b and lambda are in A074082-A074086.
Sequence in context: A118938 A007255 A003913 this_sequence A117329 A057798 A057800
Adjacent sequences: A074086 A074087 A074088 this_sequence A074090 A074091 A074092
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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 19 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Aug 21 2002
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