A048580 Pisot sequence L(3,10).

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

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: A113300 A332872 A007052 * A291292 A289612 A059738

Adjacent sequences: A048577 A048578 A048579 * A048581 A048582 A048583

Keyword

nonn

Author

David W. Wilson

Status

approved