A020739 a(n) = 2*n + 6.

6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• easy

Comments

Pisot sequence T(6,8).

Trivial case of a Pisot sequence satisfying a simple linear recurrence. Here, since round((2*n+2)^2/(2*n)^2) = 2*n + round((n+1)/n^2) = 2*n for n > 2, a(n) is even and a(n) = a(n-1) + 2. - Ralf Stephan, Sep 03 2013

Links

• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Subsequence of A005843. See A008776 for definitions of Pisot sequences.

Cf. A009056, A028557.

Programs

Mathematica

2*Range[0,70]+6 (* or *) Range[6,138,2] (* Harvey P. Dale, Apr 24 2017 *)

Formula

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

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

G.f.: 2*(3 - 2*x)/(1 - x)^2.

E.g.f.: 2*exp(x)*(3 + x).

a(n) = 2*A009056(n+1) = A028557(n+1) - A028557(n). (End)

Extensions

Better name from Ralf Stephan, Sep 03 2013