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A192778
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Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+3x+1.
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6
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0, 1, 0, 5, 4, 28, 48, 183, 424, 1315, 3420, 9864, 26756, 75237, 207128, 577345, 1597624, 4439764, 12307388, 34166643, 94769936, 262998791, 729644824, 2024614928, 5617339496, 15586328073, 43245649904, 119991232893, 332929027020
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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)+6*a(n-2)-a(n-3)-6*a(n-4)+a(n-5)+a(n-6).
G.f.: x^2*(x^2+x-1)/((x^2-x-1)*(x^4+2*x^3-3*x^2-2*x+1)). [Colin Barker, Nov 23 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+5x+1
F5(x)=x^4+3x^2+1 -> 7x^2+4x+2, so that
A192777=(1,0,1,1,2,...), A192778=(0,1,0,5,4,...), A192779=(0,0,1,1,7,...)
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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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