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A078007
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Expansion of (1-x)/(1-x-2*x^2-x^3).
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4
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1, 0, 2, 3, 7, 15, 32, 69, 148, 318, 683, 1467, 3151, 6768, 14537, 31224, 67066, 144051, 309407, 664575, 1427440, 3065997, 6585452, 14144886, 30381787, 65257011, 140165471, 301061280, 646649233, 1388937264, 2983297010, 6407820771, 13763352055, 29562290607
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OFFSET
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0,3
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COMMENTS
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Let X = the 3x3 matrix [0,1,0; 0,0,1; 1,2,1]. a(n) = center term of X^n; but A002478(n) = term (3,3) of X^n. - Gary W. Adamson, May 30 2008
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LINKS
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FORMULA
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MATHEMATICA
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LinearRecurrence[{1, 2, 1}, {1, 0, 2}, 40] (* or *) CoefficientList[Series[(1 -x)/(1-x-2*x^2-x^3), {x, 0, 40}], x] (* G. C. Greubel, Jun 28 2019 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-x-2*x^2-x^3) )); // G. C. Greubel, Jun 28 2019
(Sage) ((1-x)/(1-x-2*x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 28 2019
(GAP) a:=[1, 0, 2];; for n in [4..40] do a[n]:=a[n-1]+2*a[n-2]+a[n-3]; od; a; # G. C. Greubel, Jun 28 2019
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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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