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A192799
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Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2.
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6
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0, 1, 0, 2, 2, 5, 12, 22, 54, 109, 242, 520, 1118, 2427, 5218, 11290, 24352, 52579, 113526, 245038, 529068, 1142087, 2465644, 5322896, 11491188, 24807721, 53555508, 115617714, 249599214, 538843277, 1163273304, 2511313222, 5421508714
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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a(n) = a(n-1)+3*a(n-2)-3*a(n-4)+a(n-5)+a(n-6).
G.f.: x^2*(x^2+x-1)/(x^6+x^5-3*x^4+3*x^2+x-1). [Colin Barker, Jul 27 2012]
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EXAMPLE
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The first five polynomials p(n,x) and their reductions:
F1(x)=1 -> 1
F2(x)=x -> x
F3(x)=x^2+1 -> x^2+1
F4(x)=x^3+2x -> x^2+2x+2
F5(x)=x^4+3x^2+1 -> 4x^2+2*x+3, so that
A192798=(1,0,1,2,3,...), A192799=(0,1,0,2,2,...), A192800=(0,0,1,1,4,...)
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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