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A020727
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Pisot sequence P(2,7): a(0)=2, a(1)=7, thereafter a(n+1) is the nearest integer to a(n)^2/a(n-1).
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5
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2, 7, 24, 82, 280, 956, 3264, 11144, 38048, 129904, 443520, 1514272, 5170048, 17651648, 60266496, 205762688, 702517760, 2398545664, 8189147136, 27959497216, 95459694592, 325919783936, 1112759746560, 3799199418368, 12971278180352, 44286713884672
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OFFSET
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0,1
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COMMENTS
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It appears that a(n) = 4*a(n-1) - 2*a(n-2) (holds at least up to n = 1000 but is not known to hold in general).
The recurrence holds up to n = 10^5. - Ralf Stephan, Sep 03 2013
Empirical g.f.: (2-x)/(1-4*x+2*x^2). - Colin Barker, Feb 21 2012
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LINKS
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MATHEMATICA
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RecurrenceTable[{a[0] == 2, a[1] == 7, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 30}] (* Bruno Berselli, Feb 04 2016 *)
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PROG
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(Magma) Iv:=[2, 7]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..30]]; // Bruno Berselli, Feb 04 2016
(PARI) pisotP(nmax, a1, a2) = {
a=vector(nmax); a[1]=a1; a[2]=a2;
for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]-1/2));
a
}
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CROSSREFS
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It appears that this is a subsequence of A003480.
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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EXTENSIONS
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STATUS
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approved
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