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A074354
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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)=(1,2).
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5
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0, 0, 0, 0, 0, 14, 64, 218, 692, 1982, 5496, 14562, 37692, 95142, 236032, 576074, 1387780, 3304078, 7787656, 18190386, 42151116, 96972534, 221651472, 503650970, 1138286740, 2559944414, 5731095704, 12776843138, 28374100572
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OFFSET
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0,6
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COMMENTS
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Coefficient of q^0 is A001045(n+1).
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LINKS
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FORMULA
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G.f.: 2*x^5*(1 + 2*x)*(7 - 10*x - 13*x^2 + 12*x^3 + 12*x^4) / ((1 + x)^4*(1 - 2*x)^4).
a(n) = 4*a(n-1) + 2*a(n-2) - 20*a(n-3) - a(n-4) + 40*a(n-5) + 8*a(n-6) - 32*a(n-7) - 16*a(n-8) for n>10.
(End)
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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 0,0,0,0,0,14.
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CROSSREFS
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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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STATUS
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approved
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