A047311 Numbers that are congruent to {4, 5, 6} mod 7.

4, 5, 6, 11, 12, 13, 18, 19, 20, 25, 26, 27, 32, 33, 34, 39, 40, 41, 46, 47, 48, 53, 54, 55, 60, 61, 62, 67, 68, 69, 74, 75, 76, 81, 82, 83, 88, 89, 90, 95, 96, 97, 102, 103, 104, 109, 110, 111, 116, 117, 118, 123, 124, 125, 130, 131, 132, 137, 138, 139, 144

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*(4+x+x^2+x^3) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 25 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+3-12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047311:=n->(21*n+3-12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047311(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {4, 5, 6, 11}, 60] (* Harvey P. Dale, Oct 29 2014 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [4..6]]; // Wesley Ivan Hurt, Jun 07 2016

Crossrefs

Sequence in context: A162415 A007606 A284513 * A224081 A347269 A316783

Adjacent sequences: A047308 A047309 A047310 * A047312 A047313 A047314

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved