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Numbers that are congruent to {3, 4, 7} mod 8.
1

%I #10 Sep 08 2022 08:44:57

%S 3,4,7,11,12,15,19,20,23,27,28,31,35,36,39,43,44,47,51,52,55,59,60,63,

%T 67,68,71,75,76,79,83,84,87,91,92,95,99,100,103,107,108,111,115,116,

%U 119,123,124,127,131,132,135,139,140,143,147,148,151,155,156,159

%N Numbers that are congruent to {3, 4, 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 From _Wesley Ivan Hurt_, Jun 09 2016: (Start)

%F G.f.: x*(3+x+3*x^2+x^3)/((x-1)^2*(1+x+x^2)).

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

%F a(n) = (24*n-6-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

%F a(3k) = 8k-1, a(3k-1) = 8k-4, a(3k-2) = 8k-5. (End)

%p A047543:=n->(24*n-6-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047543(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016

%t Select[Range[0, 150], MemberQ[{3, 4, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [3, 4, 7]]; // _Wesley Ivan Hurt_, Jun 09 2016

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_