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A047323 Numbers that are congruent to {2, 5, 6} mod 7. 1
2, 5, 6, 9, 12, 13, 16, 19, 20, 23, 26, 27, 30, 33, 34, 37, 40, 41, 44, 47, 48, 51, 54, 55, 58, 61, 62, 65, 68, 69, 72, 75, 76, 79, 82, 83, 86, 89, 90, 93, 96, 97, 100, 103, 104, 107, 110, 111, 114, 117, 118, 121, 124, 125, 128, 131, 132, 135, 138, 139, 142 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
G.f.: x*(2+3*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-3-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 7k-1, a(3k-1) = 7k-2, a(3k-2) = 7k-5. (End)
MAPLE
A047323:=n->(21*n-3-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047323(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016
MATHEMATICA
Select[Range[0, 150], MemberQ[{2, 5, 6}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 07 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {2, 5, 6, 9}, 70] (* Harvey P. Dale, Aug 29 2017 *)
PROG
(Magma) [n : n in [0..150] | n mod 7 in [2, 5, 6]]; // Wesley Ivan Hurt, Jun 07 2016
CROSSREFS
Sequence in context: A055938 A190764 A276886 * A343076 A033292 A090500
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified May 19 13:25 EDT 2024. Contains 372694 sequences. (Running on oeis4.)