A047281 Numbers that are congruent to {0, 3, 6} mod 7.

0, 3, 6, 7, 10, 13, 14, 17, 20, 21, 24, 27, 28, 31, 34, 35, 38, 41, 42, 45, 48, 49, 52, 55, 56, 59, 62, 63, 66, 69, 70, 73, 76, 77, 80, 83, 84, 87, 90, 91, 94, 97, 98, 101, 104, 105, 108, 111, 112, 115, 118, 119, 122, 125, 126, 129, 132, 133, 136, 139, 140

Offset

1,2

Links

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

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

Formula

a(n+1) = 3*n - 2*floor(n/3). - Gary Detlefs, Mar 27 2010

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

From Wesley Ivan Hurt, Jun 07 2016: (Start)

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

a(n) = (21*n-15+6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9.

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

a(n) = Sum_{i=1..n-1} numerator(3/i). - Wesley Ivan Hurt, Feb 26 2017

Maple

seq(3*n - 2*floor(n/3), n=0..52); # Gary Detlefs, Mar 27 2010

Mathematica

Select[Range[0, 150], MemberQ[{0, 3, 6}, Mod[#, 7]]&] (* Harvey P. Dale, Oct 05 2012 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 3, 6, 7}, 70] (* Vincenzo Librandi, Feb 28 2017 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 3, 6]]; // Wesley Ivan Hurt, Jun 07 2016
(PARI) a(n)=3*n - 3 - (n-1)\3*2 \\ Charles R Greathouse IV, Feb 28 2017

Crossrefs

Sequence in context: A045412 A288215 A284625 * A182909 A269903 A191103

Adjacent sequences: A047278 A047279 A047280 * A047282 A047283 A047284

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved