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A047289 Numbers that are congruent to {0, 4, 6} mod 7. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)