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A124312
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Expansion of g.f. x^3*(1 - x)/(1 - x - x^2 - x^3 - x^4 - x^5).
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4
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0, 0, 1, 0, 1, 2, 4, 8, 15, 30, 59, 116, 228, 448, 881, 1732, 3405, 6694, 13160, 25872, 50863, 99994, 196583, 386472, 759784, 1493696, 2936529, 5773064, 11349545, 22312618, 43865452, 86237208, 169537887, 333302710, 655255875, 1288199132
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OFFSET
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1,6
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COMMENTS
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Second column of the n-th power of pentanacci matrix {{1,1,1,1,1},{1,0,0,0,0}, {0,1,0,0,0}, {0,0,1,0,0}, {0,0,0,1,0}} read from bottom to top gives 5 numbers starting from position n.
a(n+5) equals the number of n-length binary words avoiding runs of zeros of lengths 5i+4, (i=0,1,2,...). - Milan Janjic, Feb 26 2015
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LINKS
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MAPLE
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f:= gfun:-rectoproc({a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)-a(n+5), a(0) = 0, a(1) = 0, a(2) = 0, a(3) = 1, a(4) = 0}, a(n), remember):
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MATHEMATICA
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CoefficientList[Series[(x^3-x^4)/(1-x-x^2-x^3-x^4-x^5), {x, 0, 50}], x]
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 50); [0, 0] cat Coefficients(R!( x^3*(1-x)^2/(1-2*x+x^6) )); // G. C. Greubel, Aug 25 2023
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x^2*(1-x)^2/(1-2*x+x^6) ).list()
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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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EXTENSIONS
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STATUS
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approved
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