A047349 Numbers that are congruent to {0, 2, 4} mod 7.

0, 2, 4, 7, 9, 11, 14, 16, 18, 21, 23, 25, 28, 30, 32, 35, 37, 39, 42, 44, 46, 49, 51, 53, 56, 58, 60, 63, 65, 67, 70, 72, 74, 77, 79, 81, 84, 86, 88, 91, 93, 95, 98, 100, 102, 105, 107, 109, 112, 114, 116, 119, 121, 123, 126, 128, 130, 133, 135, 137, 140, 142

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Programs

Magma

[n : n in [0..150] | n mod 7 in [0, 2, 4]]; // Wesley Ivan Hurt, Jun 10 2016

Maple

seq(floor(n/3)+2*n, n=0..52); # Gary Detlefs, Mar 27 2010

Mathematica

Select[Range[0, 150], MemberQ[{0, 2, 4}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)

Formula

a(n+1) = floor(n/3)+2*n. - Gary Detlefs, Mar 27 2010

G.f.: x^2*(2+2*x+3*x^2)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

a(n) = n + floor(4*(n-1)/3) - 1. - Arkadiusz Wesolowski, Sep 18 2012

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

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

a(n) = (21*n-24-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

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