A047289 Numbers that are congruent to {0, 4, 6} mod 7.

0, 4, 6, 7, 11, 13, 14, 18, 20, 21, 25, 27, 28, 32, 34, 35, 39, 41, 42, 46, 48, 49, 53, 55, 56, 60, 62, 63, 67, 69, 70, 74, 76, 77, 81, 83, 84, 88, 90, 91, 95, 97, 98, 102, 104, 105, 109, 111, 112, 116, 118, 119, 123, 125, 126, 130, 132, 133, 137, 139, 140

Offset

1,2

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

From Colin Barker, Mar 13 2012: (Start)

G.f.: x*(4+2*x+x^2)/((1-x)^2*(1+x+x^2)).

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

a(n) = Sum_{i=1..n} 2^(-i mod 3). - Wesley Ivan Hurt, Jul 08 2014

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

a(n) = (21*n-12+3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9.

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

Maple

A047289:=n->(21*n-12+3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047289(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Cases[Range[0, 123], n_ /; MatchQ[Mod[n, 7], 0 | 4 | 6]] (* Jean-François Alcover, Mar 16 2011 *)
Select[Range[0, 125], MemberQ[{0, 4, 6}, Mod[#, 7]]&] (* Vincenzo Librandi, Apr 26 2012 *)

Prog

(Magma) I:=[0, 4, 6, 7]; [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

Crossrefs

Cf. A153727.

Sequence in context: A206775 A287157 A102140 * A345717 A022436 A102139

Adjacent sequences: A047286 A047287 A047288 * A047290 A047291 A047292

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, Jul 08 2014

Status

approved