A047292 Numbers that are congruent to {2, 4, 6} mod 7.

2, 4, 6, 9, 11, 13, 16, 18, 20, 23, 25, 27, 30, 32, 34, 37, 39, 41, 44, 46, 48, 51, 53, 55, 58, 60, 62, 65, 67, 69, 72, 74, 76, 79, 81, 83, 86, 88, 90, 93, 95, 97, 100, 102, 104, 107, 109, 111, 114, 116, 118, 121, 123, 125, 128, 130, 132, 135, 137, 139, 142, 144

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Programs

Magma

I:=[2, 4, 6, 9]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Apr 26 2012

Maple

A047292:=n->(21*n-6-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047292(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0,125], MemberQ[{2,4,6}, Mod[#,7]]&] (* Vincenzo Librandi, Apr 26 2012 *)
LinearRecurrence[{1,0,1,-1},{2,4,6,9},70] (* Harvey P. Dale, Feb 06 2019 *)

PARI

a(n) = 2*n + ceil(n/3) - 1; /* Joerg Arndt, Sep 20 2012 */

Formula

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = floor((7*n-1)/3). [Gary Detlefs, May 14 2011]

G.f.: x*(2+2*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2)). [Colin Barker, Mar 13 2012]

a(n) = 2*n + ceiling(n/3) - 1. - Arkadiusz Wesolowski, Sep 19 2012

From Wesley Ivan Hurt, Jun 10 2016: (Start)

a(n) = (21*n-6-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-1, a(3k-1) = 7k-3, a(3k-2) = 7k-5. (End)