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A077942
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Expansion of 1/(1-2*x+x^2+2*x^3).
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3
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1, 2, 3, 2, -3, -14, -29, -38, -19, 58, 211, 402, 477, 130, -1021, -3126, -5491, -5814, 115, 17026, 45565, 73874, 68131, -28742, -273363, -654246, -977645, -754318, 777501, 4264610, 9260355, 12701098, 7612621, -15996566, -65007949, -129244574, -161488067, -63715662, 292545891
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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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a(n) = Sum_{k=0..(n+1)/2} binomial(n+1-k,2k+1)*(-2)^k, n>=0. - Taras Goy, Apr 15 2020
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MAPLE
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seq(coeff(series(1/(1-2*x+x^2+2*x^3), x, n+1), x, n), n = 0..40); # G. C. Greubel, Aug 05 2019
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MATHEMATICA
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LinearRecurrence[{2, -1, -2}, {1, 2, 3}, 40] (* or *) CoefficientList[Series[ 1/(1-2*x+x^2+2*x^3), {x, 0, 40}], x] (* G. C. Greubel, Aug 05 2019 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-2*x+x^2+2*x^3) )); // G. C. Greubel, Aug 05 2019
(Sage) (1/(1-2*x+x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Aug 05 2019
(GAP) a:=[1, 2, 3];; for n in [4..40] do a[n]:=2*a[n-1]-a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Aug 05 2019
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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