%I #19 Sep 08 2022 08:44:57

%S 4,5,6,12,13,14,20,21,22,28,29,30,36,37,38,44,45,46,52,53,54,60,61,62,

%T 68,69,70,76,77,78,84,85,86,92,93,94,100,101,102,108,109,110,116,117,

%U 118,124,125,126,132,133,134,140,141,142,148,149,150,156,157

%N Numbers that are congruent to {4, 5, 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*(4+x+x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 07 2011

%F a(n) = 5*A002264(n-1)+n+3 = A047475(n)+3. - _Bruno Berselli_, Dec 07 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-3-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

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

%p A047429:=n->(24*n-3-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047429(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016

%t Select[Range[134], MemberQ[{4, 5, 6}, Mod[#, 8]]&] (* _Bruno Berselli_, Dec 07 2011 *)

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

%Y Cf. A002264, A047475.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_