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A047536 Numbers that are congruent to {0, 4, 7} mod 8.

%I A047536 #19 Sep 08 2022 08:44:57
%S A047536 0,4,7,8,12,15,16,20,23,24,28,31,32,36,39,40,44,47,48,52,55,56,60,63,
%T A047536 64,68,71,72,76,79,80,84,87,88,92,95,96,100,103,104,108,111,112,116,
%U A047536 119,120,124,127,128,132,135,136,140,143,144,148,151,152,156,159
%N A047536 Numbers that are congruent to {0, 4, 7} mod 8.
%H A047536 G. C. Greubel, <a href="/A047536/b047536.txt">Table of n, a(n) for n = 1..1000</a>
%H A047536 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047536 From _Chai Wah Wu_, May 29 2016: (Start)
%F A047536 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A047536 G.f.: x^2*(x^2 + 3*x + 4)/(x^4 - x^3 - x + 1). (End)
%F A047536 From _Wesley Ivan Hurt_, Jun 10 2016: (Start)
%F A047536 a(n) = (24*n-15+6*cos(2*n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/9.
%F A047536 a(3k) = 8k-1, a(3k-1) = 8k-4, a(3k-2) = 8k-8. (End)
%p A047536 A047536:=n->(24*n-15+6*cos(2*n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047536(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016
%t A047536 LinearRecurrence[{1, 0, 1, -1}, {0, 4, 7, 8}, 50] (* _G. C. Greubel_, May 29 2016 *)
%o A047536 (Magma) [n : n in [0..150] | n mod 8 in [0, 4, 7]]; // _Wesley Ivan Hurt_, May 29 2016
%K A047536 nonn,easy
%O A047536 1,2
%A A047536 _N. J. A. Sloane_