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Numbers that are congruent to {3, 4, 6} mod 8.
1

%I #14 Sep 08 2022 08:44:57

%S 3,4,6,11,12,14,19,20,22,27,28,30,35,36,38,43,44,46,51,52,54,59,60,62,

%T 67,68,70,75,76,78,83,84,86,91,92,94,99,100,102,107,108,110,115,116,

%U 118,123,124,126,131,132,134,139,140,142,147,148,150,155,156,158

%N Numbers that are congruent to {3, 4, 6} 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*(3+x+2*x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 05 2011

%F From _Wesley Ivan Hurt_, Jun 09 2016: (Start)

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

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

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

%p A047413:=n->(24*n-9-9*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047413(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016

%t Select[Range[0, 150], MemberQ[{3, 4, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [3, 4, 6]]; // _Wesley Ivan Hurt_, Jun 09 2016

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_