A047347 Numbers that are congruent to {0, 1, 4} mod 7.

0, 1, 4, 7, 8, 11, 14, 15, 18, 21, 22, 25, 28, 29, 32, 35, 36, 39, 42, 43, 46, 49, 50, 53, 56, 57, 60, 63, 64, 67, 70, 71, 74, 77, 78, 81, 84, 85, 88, 91, 92, 95, 98, 99, 102, 105, 106, 109, 112, 113, 116, 119, 120, 123, 126, 127, 130, 133, 134, 137, 140, 141

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, 1, 4]]; // Wesley Ivan Hurt, Jun 10 2016

Maple

A047347:=n->7*n/3-3+4*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047347(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0,200], MemberQ[{0,1,4}, Mod[#,7]]&] (* or *) LinearRecurrence[{1,0,1,-1}, {0,1,4,7}, 100] (* Harvey P. Dale, Dec 05 2012 *)

Formula

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

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

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

a(n) = 7*n/3-3+4*sin(2*n*Pi/3)/(3*sqrt(3)).

a(3k) = 7k-3, a(3k-1) = 7k-6, a(3k-2) = 7k-7. (End)