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

0,1

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).

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)

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 *)

Prog

(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

Crossrefs

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

Cf. A016825, A028560.

Sequence in context: A295299 A066669 A059808 * A193071 A329112 A347886

Adjacent sequences: A020739 A020740 A020741 * A020743 A020744 A020745

Keyword

nonn,easy

Author

David W. Wilson

Status

approved