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A021001
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Pisot sequence P(2,9).
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4
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2, 9, 40, 178, 792, 3524, 15680, 69768, 310432, 1381264, 6145920, 27346208, 121676672, 541399104, 2408949760, 10718597248, 47692288512, 212206348544, 944209971200, 4201252581888, 18693430269952, 83176226243584, 370091765514240, 1646719514544128
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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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Pisot sequence P(x, y): a(0) = x, a(1) = y, a(n) = roundDown(a(n-1)^2/a(n-2)) = ceiling(a(n-1)^2/a(n-2) - 1/2).
Appears to satisfy a(n) = 4*a(n-1) + 2*a(n-2).
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MATHEMATICA
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RecurrenceTable[{a[0] == 2, a[1] == 9, a[n] == Ceiling[a[n - 1]^2/a[n - 2]-1/2]}, a, {n, 0, 30}] (* _Bruno Berselli_, Feb 04 2016 *)
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PROG
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(PARI) lista(nn) = {print1(x = 2, ", ", y = 9, ", "); for (n=1, nn, z = ceil(y^2/x -1/2); print1(z, ", "); x = y; y = z; ); } \\ _Michel Marcus_, Feb 04 2016
(Magma) Iv:=[2, 9]; [n le 2 select Iv[n] else Ceiling(Self(n-1)^2/Self(n-2)-1/2): n in [1..30]]; // _Bruno Berselli_, Feb 04 2016
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CROSSREFS
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See A008776 for definitions of Pisot sequences.
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KEYWORD
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nonn
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AUTHOR
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_R. K. Guy_
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STATUS
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approved
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