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A138495
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First differences of A138477.
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2
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0, 1, 1, 1, 3, 9, 15, 25, 55, 121, 231, 441, 903, 1849, 3655, 7225, 14535, 29241, 58311, 116281, 232903, 466489, 932295, 1863225, 3727815, 7458361, 14913991, 29822521, 59650503, 119311929, 238612935, 477204025, 954429895, 1908903481, 3817763271, 7635439161, 15270965703
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OFFSET
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0,5
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LINKS
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FORMULA
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O.g.f.: x/((1-2*x)*(1+x)*(1+2*x^2)).
a(n) = a(n-1) + 2*a(n-3) + 4*a(n-4). (End)
E.g.f.: (2*exp(2*x) - exp(-x) - cos(sqrt(2)*x) + 2*sqrt(2)*sin(sqrt(2)*x) )/9. - G. C. Greubel, May 24 2019
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MATHEMATICA
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LinearRecurrence[{1, 0, 2, 4}, {0, 1, 1, 1}, 40] (* G. C. Greubel, May 24 2019 *)
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PROG
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(PARI) concat(0, Vec(x/((1-2*x)*(1+x)*(1+2*x^2)) + O(x^40))) \\ Michel Marcus, May 24 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( x/((1-2*x)*(1+x)*(1+2*x^2)) )); // G. C. Greubel, May 24 2019
(Sage) (x/((1-2*x)*(1+x)*(1+2*x^2))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019
(GAP) a:=[0, 1, 1, 1];; for n in [5..40] do a[n]:=a[n-1]+2*a[n-3]+4*a[n-4]; od; a; # G. C. Greubel, May 24 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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