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A047556 Numbers that are congruent to {3, 6, 7} mod 8. 2

%I

%S 3,6,7,11,14,15,19,22,23,27,30,31,35,38,39,43,46,47,51,54,55,59,62,63,

%T 67,70,71,75,78,79,83,86,87,91,94,95,99,102,103,107,110,111,115,118,

%U 119,123,126,127,131,134,135,139,142,143,147,150,151,155,158,159

%N Numbers that are congruent to {3, 6, 7} mod 8.

%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+x)*(x^2+3) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 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) = (24*n-9*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.

%F a(3k) = 8k-1, a(3k-1) = 8k-2, a(3k-2) = 8k-5. (End)

%p A047556:=n->(24*n-9*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9: seq(A047556(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016

%t Select[Range[0, 150], MemberQ[{3, 6, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 10 2016 *)

%o (MAGMA) [n : n in [0..150] | n mod 8 in [3, 6, 7]]; // _Wesley Ivan Hurt_, Jun 10 2016

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

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Last modified May 20 03:10 EDT 2019. Contains 323412 sequences. (Running on oeis4.)