A020743 Pisot sequence L(7,10).

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
• easy

Links

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

Crossrefs

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

Cf. A020717.

Programs

Mathematica

LinearRecurrence[{2,0,-1},{7,10,15},40] (* Harvey P. Dale, Jun 10 2022 *)

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, 7, 10) \\ Colin Barker, Aug 07 2016

Formula

a(n) = Fib(n+5)+2 = A157725(n+5). a(n) = 2a(n-1) - a(n-3).