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

1,3

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).

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

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 *)

Prog

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

Crossrefs

Cf. A030341.

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

Sequence in context: A287515 A260581 A179772 * A037455 A020675 A317303

Adjacent sequences: A047351 A047352 A047353 * A047355 A047356 A047357

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved