A047318 Numbers that are congruent to {0, 1, 2, 4, 5, 6} mod 7.

0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 81, 82, 83

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A017017. - Michel Marcus, Sep 10 2015

Links

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

Crossrefs

Cf. A017017.

Programs

Magma

[n+Floor((n-4)/6) : n in [1..100]]; // Wesley Ivan Hurt, Sep 10 2015

Magma

[n : n in [0..140] | n mod 7 in [0, 1, 2, 4, 5, 6]]; // Vincenzo Librandi, Sep 11 2015

Maple

for n from 0 to 200 do if n mod 7 <> 3 then printf(`%d,`,n) fi: od:
A047318:=n->n+floor((n-4)/6): seq(A047318(n), n=1..100); # Wesley Ivan Hurt, Sep 10 2015

Mathematica

Table[n+Floor[(n-4)/6], {n,100}] (* Wesley Ivan Hurt, Sep 10 2015 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 6, 7}, 100] (* Vincenzo Librandi, Sep 11 2015 *)
DeleteCases[Range[0,100],?(Mod[#,7]==3&)] (* _Harvey P. Dale, May 07 2016 *)

Formula

G.f.: x^2*(1+x+2*x^2+x^3+x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Dec 03 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-4)/6). (End)

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

a(n) = (42*n-39+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-2, a(6k-2) = 7k-3, a(6k-3) = 7k-5, a(6k-4) = 7k-6, a(6k-5) = 7k-7. (End)

Extensions

More terms from James Sellers, Feb 19 2001