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A052991
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Expansion of (1-x-x^2)/(1-3x-x^2).
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3
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1, 2, 6, 20, 66, 218, 720, 2378, 7854, 25940, 85674, 282962, 934560, 3086642, 10194486, 33670100, 111204786, 367284458, 1213058160, 4006458938, 13232434974, 43703763860, 144343726554, 476734943522, 1574548557120, 5200380614882, 17175690401766, 56727451820180
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (-1+x+x^2)/(-1+3*x+x^2).
Recurrence: {a(0)=1, a(1)=2, a(n)+3*a(n+1)-a(n+2), a(2)=6}.
Sum(-2/13*(3*_alpha-2)*_alpha^(-1-n), _alpha=RootOf(-1+3*_Z+_Z^2)).
G.f.: 1/Q(0), where Q(k) = 1 + x^2 - (2*k+1)*x + x*(2*k-1 - x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 05 2013
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MAPLE
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spec := [S, {S=Sequence(Prod(Sequence(Union(Prod(Z, Z), Z)), Union(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-x^2)/(1-3x-x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 1}, {1, 2, 6}, 30] (* Harvey P. Dale, May 10 2022 *)
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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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