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

Author

David W. Wilson

Keywords

• nonn

Links

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

Crossrefs

It appears that this is a subsequence of A007052.

See A008776 for definitions of Pisot sequences.

Programs

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

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 *)

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

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]