A047354 Numbers that are congruent to {0, 1, 2} mod 7.

0, 1, 2, 7, 8, 9, 14, 15, 16, 21, 22, 23, 28, 29, 30, 35, 36, 37, 42, 43, 44, 49, 50, 51, 56, 57, 58, 63, 64, 65, 70, 71, 72, 77, 78, 79, 84, 85, 86, 91, 92, 93, 98, 99, 100, 105, 106, 107, 112, 113, 114, 119, 120, 121, 126, 127, 128, 133, 134, 135, 140, 141

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3000
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -1).

Crossrefs

Cf. A030341.

Cf. similar sequences with formula n+i*floor(n/3) listed in A281899.

Programs

Magma

[n : n in [0..150] | n mod 7 in [0..2]]; // Wesley Ivan Hurt, Jun 08 2016

Maple

seq(7*floor(n/3)+(n mod 3), n=0..60); # Gary Detlefs, Mar 09 2010

Mathematica

Flatten[{#,#+1,#+2}&/@(7Range[0,20])]  (* Harvey P. Dale, Mar 05 2011 *)

Formula

a(n) = 7*floor(n/3)+(n mod 3), with offset 0 and a(0)=0. - Gary Detlefs, Mar 09 2010

From R. J. Mathar, Mar 29 2010: (Start)

G.f.: x^2*(1+x+5*x^2)/((1+x+x^2) * (x-1)^2).

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. (End)

a(n+1) = Sum_{k>=0} A030341(n,k)*b(k) with b(0)=1 and b(k)=7*3^(k-1) for k>0. - Philippe Deléham, Oct 24 2011

From Wesley Ivan Hurt, Jun 08 2016: (Start)

a(n) = (21*n-33-12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

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

a(n) = n + 4*floor((n-1)/3) - 1. - Bruno Berselli, Feb 06 2017