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A021001 Pisot sequence P(2,9). 4

%I #35 Dec 30 2023 23:43:44

%S 2,9,40,178,792,3524,15680,69768,310432,1381264,6145920,27346208,

%T 121676672,541399104,2408949760,10718597248,47692288512,212206348544,

%U 944209971200,4201252581888,18693430269952,83176226243584,370091765514240,1646719514544128

%N Pisot sequence P(2,9).

%H Colin Barker, <a href="/A021001/b021001.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>

%F 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).

%F Appears to satisfy a(n) = 4*a(n-1) + 2*a(n-2).

%t 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 *)

%o (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

%o (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

%Y See A008776 for definitions of Pisot sequences.

%K nonn

%O 0,1

%A _R. K. Guy_

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)