A047320 Numbers that are congruent to {0, 5, 6} mod 7.

0, 5, 6, 7, 12, 13, 14, 19, 20, 21, 26, 27, 28, 33, 34, 35, 40, 41, 42, 47, 48, 49, 54, 55, 56, 61, 62, 63, 68, 69, 70, 75, 76, 77, 82, 83, 84, 89, 90, 91, 96, 97, 98, 103, 104, 105, 110, 111, 112, 117, 118, 119, 124, 125, 126, 131, 132, 133, 138, 139, 140

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^2*(5+x+x^2) / ((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-9-8*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047320:=n->(21*n-9-8*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047320(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

Select[Range[0, 200], MemberQ[{0, 5, 6}, Mod[#, 7]]&] (* Harvey P. Dale, May 25 2012 *)

Prog

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

Crossrefs

Sequence in context: A037360 A120521 A022566 * A327301 A247522 A011761

Adjacent sequences: A047317 A047318 A047319 * A047321 A047322 A047323

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved