A020742 Pisot sequence T(7,9).

7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• easy

Links

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

Crossrefs

Subsequence of A005408, A020735. See A008776 for definitions of Pisot sequences.

Cf. A016825, A028560.

Essentially the same as A005818.

Programs

Mathematica

T[x_, y_, z_] := Block[{a}, a[0] = x; a[1] = y; a[n_] := a[n] = Floor[a[n - 1]^2/a[n - 2]]; Table[a[n], {n, 0, z}]]; T[7, 9, 66] (* Michael De Vlieger, Aug 08 2016 *)

PARI

pisotT(nmax, a1, a2) = {
  a=vector(nmax); a[1]=a1; a[2]=a2;
  for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]));
  a
}
pisotT(50, 7, 9) \\ Colin Barker, Aug 08 2016

Formula

a(n) = 2*n + 7.

a(n) = 2*a(n-1) - a(n-2).

From Elmo R. Oliveira, Oct 30 2024: (Start)

G.f.: (7 - 5*x)/(1 - x)^2.

E.g.f.: (7 + 2*x)*exp(x).

a(n) = A016825(n+3)/2 = A028560(n+1) - A028560(n). (End)