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A048580 Pisot sequence L(3,10). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

FORMULA

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]

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

It appears that this is a subsequence of A007052.

See A008776 for definitions of Pisot sequences.

Sequence in context: A255813 A113300 A007052 * A289612 A059738 A094832

Adjacent sequences:  A048577 A048578 A048579 * A048581 A048582 A048583

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified November 19 08:51 EST 2017. Contains 294923 sequences.