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A074085
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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)=(2,1).
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2
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0, 0, 0, 0, 5, 24, 91, 308, 978, 2978, 8802, 25440, 72251, 202316, 559941, 1534548, 4170256, 11250630, 30158900, 80389600, 213204513, 562896832, 1480086111, 3877337556, 10123000126, 26347306474, 68378847990, 176994780672
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OFFSET
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0,5
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COMMENTS
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The coefficient of q^0 is the Pell number A000129(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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Table of n, a(n) for n=0..27.
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.: (5x^4-6x^5-8x^6-2x^7)/(1-2x-x^2)^3.
a(n)=6a(n-1)-9a(n-2)-4a(n-3)+9a(n-4)+6a(n-5)+a(n-6) for n>=8.
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EXAMPLE
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The first 6 nu polynomials are nu(0)=1, nu(1)=2, nu(2)=5, nu(3)=12+2q, nu(4)=29+9q+5q^2, nu(5)=70+32q+24q^2+14q^3+2q^4, so the coefficients of q^2 are 0,0,0,0,5,24.
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MATHEMATICA
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b=2; lambda=1; expon=2; 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^3 are in A000129, A074084 and A074086. Related sequences with other values of b and lambda are in A074082-A074083 and A074087-A074089.
Sequence in context: A220316 A220339 A158499 * A145914 A066316 A180354
Adjacent sequences: A074082 A074083 A074084 * A074086 A074087 A074088
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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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STATUS
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approved
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