A047292 Numbers that are congruent to {2, 4, 6} mod 7.

2, 4, 6, 9, 11, 13, 16, 18, 20, 23, 25, 27, 30, 32, 34, 37, 39, 41, 44, 46, 48, 51, 53, 55, 58, 60, 62, 65, 67, 69, 72, 74, 76, 79, 81, 83, 86, 88, 90, 93, 95, 97, 100, 102, 104, 107, 109, 111, 114, 116, 118, 121, 123, 125, 128, 130, 132, 135, 137, 139, 142, 144

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

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

Formula

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

a(n) = floor((7*n-1)/3). [Gary Detlefs, May 14 2011]

G.f.: x*(2+2*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2)). [Colin Barker, Mar 13 2012]

a(n) = 2*n + ceiling(n/3) - 1. - Arkadiusz Wesolowski, Sep 19 2012

From Wesley Ivan Hurt, Jun 10 2016: (Start)

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

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

Maple

A047292:=n->(21*n-6-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047292(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 125], MemberQ[{2, 4, 6}, Mod[#, 7]]&] (* Vincenzo Librandi, Apr 26 2012 *)
LinearRecurrence[{1, 0, 1, -1}, {2, 4, 6, 9}, 70] (* Harvey P. Dale, Feb 06 2019 *)

Prog

(Magma) I:=[2, 4, 6, 9]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Apr 26 2012
(PARI) a(n) = 2*n + ceil(n/3) - 1; /* Joerg Arndt, Sep 20 2012 */

Crossrefs

Sequence in context: A292649 A061785 A330118 * A189930 A184627 A203988

Adjacent sequences: A047289 A047290 A047291 * A047293 A047294 A047295

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved