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A047321 Numbers that are congruent to {1, 5, 6} mod 7. 1
1, 5, 6, 8, 12, 13, 15, 19, 20, 22, 26, 27, 29, 33, 34, 36, 40, 41, 43, 47, 48, 50, 54, 55, 57, 61, 62, 64, 68, 69, 71, 75, 76, 78, 82, 83, 85, 89, 90, 92, 96, 97, 99, 103, 104, 106, 110, 111, 113, 117, 118, 120, 124, 125, 127, 131, 132, 134, 138, 139, 141 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..61.

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

FORMULA

G.f.: x*(1+4*x+x^2+x^3)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Dec 03 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-6-3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-1, a(3k-1) = 7k-2, a(3k-2) = 7k-6. (End)

MAPLE

A047321:=n->(21*n-6-3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047321(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016

MATHEMATICA

Select[Range[0, 150], MemberQ[{1, 5, 6}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 07 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 7 in [1, 5, 6]]; // Wesley Ivan Hurt, Jun 07 2016

CROSSREFS

Sequence in context: A030742 A048583 A169622 * A033158 A193569 A032721

Adjacent sequences:  A047318 A047319 A047320 * A047322 A047323 A047324

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 24 22:24 EDT 2016. Contains 275018 sequences.