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A047282 Numbers that are congruent to {1, 3, 6} mod 7. 2

%I

%S 1,3,6,8,10,13,15,17,20,22,24,27,29,31,34,36,38,41,43,45,48,50,52,55,

%T 57,59,62,64,66,69,71,73,76,78,80,83,85,87,90,92,94,97,99,101,104,106,

%U 108,111,113,115,118,120,122,125,127,129,132,134,136,139,141

%N Numbers that are congruent to {1, 3, 6} mod 7.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

%F G.f.: x*(1+2*x+3*x^2+x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 25 2011

%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)

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

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

%F a(3*k) = 7*k-1, a(3*k-1) = 7*k-4, a(3*k-2) = 7*k-6. (End)

%F a(n) = 2*n - 1 + floor(n/3). - _Wesley Ivan Hurt_, Dec 28 2016

%p A047282:=n->(21*n-12+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047282(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016

%t Select[Range[0, 150], MemberQ[{1, 3, 6}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 10 2016 *)

%o (MAGMA) [n : n in [0..150] | n mod 7 in [1, 3, 6]]; // _Wesley Ivan Hurt_, Jun 10 2016

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)