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A122099
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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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5
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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, 5165460748321
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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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Transpose[NestList[{#[[2]], Last[#], First[#]-3Last[#]}&, {1, 1, 0}, 35]][[1]] (* Harvey P. Dale, Mar 13 2011 *)
LinearRecurrence[{-3, 0, 1}, {1, 1, 0}, 40] (* G. C. Greubel, Oct 02 2019 *)
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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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