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A159340
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Transform of the finite sequence (1, 0, -1) by the T_{0,1} transformation (see link).
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4
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2, 3, 6, 16, 38, 88, 204, 474, 1102, 2562, 5956, 13846, 32188, 74828, 173954, 404394, 940102, 2185472, 5080606, 11810976, 27457188, 63830218, 148387254, 344958514, 801931252, 1864263982, 4333887956, 10075067156, 23421689538, 54448822258
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OFFSET
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0,1
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LINKS
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FORMULA
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O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2)+((1-z+z^2)/(1-3*z+2*z^2-z^3)).
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 5, with a(0)=2, a(1)=3, a(2)=6, a(3)=16, a(4)=38.
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MAPLE
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a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=38:for n from 2 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i), i=0..31);
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MATHEMATICA
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Join[{2, 3}, LinearRecurrence[{3, -2, 1}, {6, 16, 38}, 49]] (* G. C. Greubel, Jun 25 2018 *)
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PROG
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(PARI) z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2)+((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 25 2018
(Magma) I:=[6, 16, 38]; [2, 3] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 25 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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