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A159329
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Transform of the finite sequence (1, 0, -1) by the T_{1,1} transformation (see link).
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4
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2, 4, 9, 23, 54, 125, 290, 674, 1567, 3643, 8469, 19688, 45769, 106400, 247350, 575019, 1336757, 3107583, 7224254, 16794353, 39042134, 90761950, 210995935, 490506039, 1140288197, 2650848448, 6162474989, 14326016268, 33303947274
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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.: 2+4*x -x^2*(9-4*x+3*x^2) / ( -1+3*x-2*x^2+x^3 ).
a(0)=2, a(1)=4, a(2)=9, a(3)=23, a(4)=54 and for n>=2 a(n+3)=3*a(n+2)-2*a(n+1)+a(n).
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MATHEMATICA
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Join[{2, 4}, LinearRecurrence[{3, -2, 1}, {9, 23, 54}, 50]] (* G. C. Greubel, Jun 26 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(2+4*x -x^2*(9-4*x+3*x^2)/(-1+3*x-2*x^2+x^3)) \\ G. C. Greubel, Jun 26 2018
(Magma) I:=[9, 23, 54]; [2, 4] 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 26 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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