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Search: id:A074083
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| A074083 |
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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)=(1,1). |
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+0
5
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| 0, 0, 0, 0, 0, 4, 14, 39, 97, 224, 494, 1051, 2177, 4412, 8784, 17228, 33360, 63886, 121164, 227833, 425147, 787916, 1451198, 2657821, 4842727, 8782230, 15857426, 28517864, 51095760, 91232520, 162372682, 288115147, 509790277, 899630376
(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 in nu(n) is the Fibonacci number F(n+1). The coefficient of q^1 is A023610(n-3).
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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.: (4x^5-2x^6-9x^7+x^8+6x^9+2x^10)/(1-x-x^2)^4.
a(n)=4a(n-1)-2a(n-2)-8a(n-3)+5a(n-4)+8a(n-5)-2a(n-6)-4a(n-7)-a(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)=1, nu(2)=2, nu(3)=3+q, nu(4)=5+3q+2q^2, nu(5)=8+7q+6q^2+4q^3+q^4, so the coefficients of q^3 are 0,0,0,0,0,4.
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MATHEMATICA
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b=1; lambda=1; 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 A000045, A023610 and A074082. Related sequences with different values of b and lambda are in A074084-A074089.
Sequence in context: A130423 A055484 A055279 this_sequence A144141 A066375 A093160
Adjacent sequences: A074080 A074081 A074082 this_sequence A074084 A074085 A074086
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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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