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A052900
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Expansion of (1-x)/(1-x-3x^3).
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1
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1, 0, 0, 3, 3, 3, 12, 21, 30, 66, 129, 219, 417, 804, 1461, 2712, 5124, 9507, 17643, 33015, 61536, 114465, 213510, 398118, 741513, 1382043, 2576397, 4800936, 8947065, 16676256, 31079064, 57920259, 107949027, 201186219, 374946996
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: (-1+x)/(-1+x+3*x^3)
Recurrence: {a(1)=0, a(0)=1, a(2)=0, 3*a(n)+a(n+2)-a(n+3)=0}
Sum(-1/85*(2+9*_alpha^2-29*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+3*_Z^3))
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MAPLE
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spec := [S, {S=Sequence(Prod(Union(Z, Z, Z), Sequence(Z), Z, Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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CoefficientList[Series[(1-x)/(1-x-3x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 0, 3}, {1, 0, 0}, 40] (* Harvey P. Dale, Aug 05 2021 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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