A047303 Numbers that are congruent to {0, 1, 2, 3, 4, 6} mod 7.

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76

Offset

1,3

Comments

Complement of A017041. - Michel Marcus, Sep 08 2015

Links

Table of n, a(n) for n=1..66.

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

Formula

G.f.: x^2*(1+x+x^2+x^3+2*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 07 2015: (Start)

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

a(n) = n + 1 + floor((n-2)/6) - ceiling((n-1)/6) + floor((n-1)/6) - ceiling(n/6) + floor(n/6). (End)

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

a(n) = (42*n - 51 + 3*cos(n*Pi) + 4*sqrt(3)*cos((1-4*n)*Pi/6) + 12*sin((1+2*n)*Pi/6))/36.

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

Maple

A047303:=n->n+1+floor((n-2)/6)-ceil((n-1)/6)+floor((n-1)/6)-ceil(n/6)+floor(n/6): seq(A047303(n), n=1..100); # Wesley Ivan Hurt, Sep 07 2015

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 4, 6}, Mod[#, 7]] &] (* Vincenzo Librandi, Sep 08 2015 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 6, 7}, 80] (* Harvey P. Dale, Sep 24 2016 *)

Prog

(Magma) [n: n in [0..100] | n mod 7 in [0..4] cat [6]]; // Vincenzo Librandi, Sep 08 2015

Crossrefs

Cf. A017041 (7n+5).

Sequence in context: A141451 A285211 A183217 * A057906 A039214 A032866

Adjacent sequences: A047300 A047301 A047302 * A047304 A047305 A047306

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Sep 08 2015

Status

approved