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A048580
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Pisot sequence L(3,10).
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4
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3, 10, 34, 116, 396, 1352, 4616, 15760, 53808, 183712, 627232, 2141504, 7311552, 24963200, 85229696, 290992384, 993510144, 3392055808, 11581202944, 39540700160, 135000394752, 460920178688, 1573679925248, 5372879343616, 18344157523968, 62630871408640
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OFFSET
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0,1
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
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FORMULA
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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).
Empirical g.f.: (3-2*x)/(1-4*x+2*x^2). [Colin Barker, Feb 21 2012]
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MATHEMATICA
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RecurrenceTable[{a[0] == 3, a[1] == 10, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 30}] (* Bruno Berselli, Feb 05 2016 *)
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PROG
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(Magma) Lxy:=[3, 10]; [n le 2 select Lxy[n] else Ceiling(Self(n-1)^2/Self(n-2)): n in [1..30]]; // Bruno Berselli, Feb 05 2016
(PARI) pisotL(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]));
a
}
pisotL(50, 3, 10) \\ Colin Barker, Aug 07 2016
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CROSSREFS
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It appears that this is a subsequence of A007052.
See A008776 for definitions of Pisot sequences.
Sequence in context: A113300 A332872 A007052 * A291292 A289612 A059738
Adjacent sequences: A048577 A048578 A048579 * A048581 A048582 A048583
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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