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A020748
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Pisot sequence T(4,10), a(n) = floor(a(n-1)^2/a(n-2)).
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2
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4, 10, 25, 62, 153, 377, 928, 2284, 5621, 13833, 34042, 83774, 206159, 507335, 1248496, 3072412, 7560869, 18606469, 45788478, 112680418, 277294139, 682390435, 1679287948, 4132543288, 10169735361, 25026602289, 61587720810, 151560619806, 372974046999
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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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G.f.: (-3x^5+2x^4+x^3-x^2-2x+4)/[(1-x)(1-2x-x^2-2x^5)] (conjectured). - Ralf Stephan, May 12 2004
Note the warning in A010925 from Pab Ter (pabrlos(AT)yahoo.com), May 23 2004: [A010925] and other examples show that it is essential to reject conjectured generating functions for Pisot sequences until a proof or reference is provided. - N. J. A. Sloane, Jul 26 2016
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MATHEMATICA
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RecurrenceTable[{a[0]==4, a[1]==10, a[n]==Floor[a[n-1]^2/a[n-2]]}, a, {n, 30}] (* Harvey P. Dale, Dec 26 2016 *)
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PROG
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(PARI) pisotT(nmax, a1, a2) = {
a=vector(nmax); a[1]=a1; a[2]=a2;
for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]));
a
}
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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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STATUS
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approved
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