login
Numbers that are congruent to {4, 6, 7} mod 8.
1

%I #12 Sep 08 2022 08:44:57

%S 4,6,7,12,14,15,20,22,23,28,30,31,36,38,39,44,46,47,52,54,55,60,62,63,

%T 68,70,71,76,78,79,84,86,87,92,94,95,100,102,103,108,110,111,116,118,

%U 119,124,126,127,132,134,135,140,142,143,148,150,151,156,158

%N Numbers that are congruent to {4, 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*(4+2*x+x^2+x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Nov 06 2015

%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+3-12*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.

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

%p A047506:=n->(24*n+3-12*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047506(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016

%t Select[Range[0, 150], MemberQ[{4, 6, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [4, 6, 7]]; // _Wesley Ivan Hurt_, Jun 09 2016

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_