A048584 Pisot sequence L(5,7).

5, 7, 10, 15, 23, 36, 57, 91, 146, 235, 379, 612, 989, 1599, 2586, 4183, 6767, 10948, 17713, 28659, 46370, 75027, 121395, 196420, 317813, 514231, 832042, 1346271, 2178311, 3524580, 5702889, 9227467, 14930354, 24157819, 39088171, 63245988, 102334157, 165580143

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Comments

a(n)= BA^(n)B(1), n>=0, with compositions of Wythoff's complementary A(n):=A000201(n) and B(n)=A001950(n) sequences. See the W. Lang link under A135817 for the Wythoff representation of numbers (with A as 1 and B as 0 and the argument 1 omitted). E.g. 5=`00`, 7=`010`, 10=`0110`, 15=`01110`,..., in Wythoff code.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Crossrefs

Subsequence of A018910. See A008776 for definitions of Pisot sequences.

Programs

Mathematica

LinearRecurrence[{2,0,-1},{5,7,10},40] (* Harvey P. Dale, Oct 02 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, 5, 7) \\ Colin Barker, Aug 07 2016

Formula

a(n) = Fib(n+4)+2. a(n) = 2a(n-1) - a(n-3).

a(n)=A020743(n-1), n>0. - R. J. Mathar, Oct 15 2008