A047321 Numbers that are congruent to {1, 5, 6} mod 7.

1, 5, 6, 8, 12, 13, 15, 19, 20, 22, 26, 27, 29, 33, 34, 36, 40, 41, 43, 47, 48, 50, 54, 55, 57, 61, 62, 64, 68, 69, 71, 75, 76, 78, 82, 83, 85, 89, 90, 92, 96, 97, 99, 103, 104, 106, 110, 111, 113, 117, 118, 120, 124, 125, 127, 131, 132, 134, 138, 139, 141

Offset

1,2

Links

Table of n, a(n) for n=1..61.

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

Formula

G.f.: x*(1+4*x+x^2+x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 03 2011

From Wesley Ivan Hurt, Jun 07 2016: (Start)

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

a(n) = (21*n-6-3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047321:=n->(21*n-6-3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047321(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

Select[Range[0, 150], MemberQ[{1, 5, 6}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 07 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [1, 5, 6]]; // Wesley Ivan Hurt, Jun 07 2016

Crossrefs

Sequence in context: A030742 A048583 A169622 * A033158 A193569 A032721

Adjacent sequences: A047318 A047319 A047320 * A047322 A047323 A047324

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved