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A022039
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Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(8,65).
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1
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8, 65, 528, 4288, 34823, 282798, 2296605, 18650749, 151462893, 1230031456, 9989096027, 81121534697, 658788680558, 5350028537458, 43447627739097, 352838558325161, 2865404964997647, 23269978350457597, 188975694202166613, 1534673236964508227
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OFFSET
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0,1
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COMMENTS
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This coincides with the Pisot T(8,65) sequence as defined in A008776 at least up to n <= 14000. - R. J. Mathar, Feb 13 2016
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LINKS
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FORMULA
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Empirical g.f.: -(x^6+x^5+x^4+x^3-x-8) / (x^7+x^6+x^5+x^4-x^2-8*x+1). - Colin Barker, Dec 02 2014
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MATHEMATICA
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RecurrenceTable[{a[1] == 8, a[2] == 65, a[n] == Ceiling[a[n-1]^2/a[n-2]] - 1}, a, {n, 30}] (* Bruno Berselli, Feb 17 2016 *)
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PROG
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(PARI)
T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=floor(a[n-1]^2/a[n-2])); a
(Magma) Tiv:=[8, 65]; [n le 2 select Tiv[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..30]]; // Bruno Berselli, Feb 17 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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