A047323 Numbers that are congruent to {2, 5, 6} mod 7.

2, 5, 6, 9, 12, 13, 16, 19, 20, 23, 26, 27, 30, 33, 34, 37, 40, 41, 44, 47, 48, 51, 54, 55, 58, 61, 62, 65, 68, 69, 72, 75, 76, 79, 82, 83, 86, 89, 90, 93, 96, 97, 100, 103, 104, 107, 110, 111, 114, 117, 118, 121, 124, 125, 128, 131, 132, 135, 138, 139, 142

Offset

1,1

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

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

Maple

A047323:=n->(21*n-3-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047323(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

Select[Range[0, 150], MemberQ[{2, 5, 6}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 07 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {2, 5, 6, 9}, 70] (* Harvey P. Dale, Aug 29 2017 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [2, 5, 6]]; // Wesley Ivan Hurt, Jun 07 2016

Crossrefs

Sequence in context: A055938 A190764 A276886 * A343076 A033292 A090500

Adjacent sequences: A047320 A047321 A047322 * A047324 A047325 A047326

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved