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A122100
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a(n) = 3*a(n-1) - a(n-3) for n>2, with a(0)=1, a(1)=-1, a(2)=0.
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7
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1, -1, 0, -1, -2, -6, -17, -49, -141, -406, -1169, -3366, -9692, -27907, -80355, -231373, -666212, -1918281, -5523470, -15904198, -45794313, -131859469, -379674209, -1093228314, -3147825473, -9063802210, -26098178316, -75146709475, -216376326215, -623030800329, -1793945691512
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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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G.f.: (1-4*x+3*x^2)/(1-3*x+x^3).
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MAPLE
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seq(coeff(series((1-4*x+3*x^2)/(1-3*x+x^3), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Oct 02 2019
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MATHEMATICA
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LinearRecurrence[{3, 0, -1}, {1, -1, 0}, 40] (* Harvey P. Dale, Nov 14 2014 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-4*x+3*x^2)/(1-3*x+x^3) )); // G. C. Greubel, Oct 02 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-4*x+3*x^2)/(1-3*x+x^3)).list()
(GAP) a:=[1, -1, 0];; for n in [4..40] do a[n]:=3*a[n-1]-a[n-3]; od; a; # G. C. Greubel, Oct 02 2019
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CROSSREFS
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KEYWORD
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sign,easy,less
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AUTHOR
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STATUS
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approved
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