A047306 Numbers that are congruent to {0, 2, 3, 4, 5, 6} mod 7.

0, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77

Offset

1,2

Comments

Complement of A016993. - Michel Marcus, Sep 10 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x^2*(2+x+x^2+x^3+x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Sep 10 2015: (Start)

a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

a(n) = n + floor((n-2)/6). (End)

From Wesley Ivan Hurt, Jun 15 2016: (Start)

a(n) = (42*n-27+3*cos(n*Pi)-12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/36.

a(6k) = 7k-1, a(6k-1) = 7k-2, a(6k-2) = 7k-3, a(6k-3) = 7k-4, a(6k-4) = 7k-5, a(6k-5) = 7k-7. (End)

Maple

A047306:=n->n+floor((n-2)/6): seq(A047306(n), n=1..100); # Wesley Ivan Hurt, Sep 10 2015

Mathematica

Select[Range[0, 100], MemberQ[{0, 2, 3, 4, 5, 6}, Mod[#, 7]] &] (* Vincenzo Librandi, Oct 22 2014 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 2, 3, 4, 5, 6, 7}, 70] (* Harvey P. Dale, May 28 2018 *)

Prog

(PARI) concat(0, Vec(x^2*(2+x+x^2+x^3+x^4+x^5)/((1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2) + O(x^30))) \\ Michel Marcus, Oct 22 2014
(Magma) [n: n in [0..100] | n mod 7 in [0] cat [2..6]]; // Vincenzo Librandi, Oct 22 2014

Crossrefs

Cf. A016993.

Sequence in context: A091249 A154799 A020660 * A332108 A316228 A353935

Adjacent sequences: A047303 A047304 A047305 * A047307 A047308 A047309

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Michel Marcus, Oct 22 2014

Status

approved