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Search: id:A074087
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| A074087 |
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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)=(2,3). |
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+0
6
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| 0, 0, 0, 6, 33, 144, 570, 2118, 7587, 26448, 90420, 304470, 1013061, 3338112, 10911150, 35423862, 114342855, 367242336, 1174368360, 3741029094, 11876859369, 37591894320, 118659631650, 373630740966, 1173847761003
(list; graph; listen)
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OFFSET
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0,4
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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.: (6x^3+9x^4)/(1-2x-3x^2)^2.
a(n)=4a(n-1)+2a(n-2)-12a(n-3)-9a(n-4) for n>=5.
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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^1 are 0,0,0,6,33,144.
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MATHEMATICA
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b=2; lambda=3; expon=1; 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^2 and q^3 are in A014983, A074088 and A074089. Related sequences with other values of b and lambda are in A074082-A074086.
Sequence in context: A073375 A089097 A120009 this_sequence A022730 A099432 A072260
Adjacent sequences: A074084 A074085 A074086 this_sequence A074088 A074089 A074090
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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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