|
%I #10 Sep 08 2022 08:44:57
%S 2,4,5,10,12,13,18,20,21,26,28,29,34,36,37,42,44,45,50,52,53,58,60,61,
%T 66,68,69,74,76,77,82,84,85,90,92,93,98,100,101,106,108,109,114,116,
%U 117,122,124,125,130,132,133,138,140,141,146,148,149,154,156,157
%N Numbers that are congruent to {2, 4, 5} 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*(2+2*x+x^2+3*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-15-12*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 8k-3, a(3k-1) = 8k-4, a(3k-2) = 8k-6. (End)
%p A047611:=n->(24*n-15-12*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047611(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016
%t Select[Range[0, 150], MemberQ[{2, 4, 5}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [2, 4, 5]]; // _Wesley Ivan Hurt_, Jun 09 2016
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
|
