|
%I #15 Sep 08 2022 08:44:57
%S 0,1,6,8,9,14,16,17,22,24,25,30,32,33,38,40,41,46,48,49,54,56,57,62,
%T 64,65,70,72,73,78,80,81,86,88,89,94,96,97,102,104,105,110,112,113,
%U 118,120,121,126,128,129,134,136,137,142,144,145,150,152,153,158
%N Numbers that are congruent to {0, 1, 6} mod 8.
%H Vincenzo Librandi, <a href="/A047394/b047394.txt">Table of n, a(n) for n = 1..3000</a>
%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^2*(1+5*x+2*x^2)/((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) = 8*n/3-3+cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)).
%F a(3k) = 8k-2, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)
%p A047394:=n->8*n/3-3+cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047394(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016
%t Select[Range[0, 150], MemberQ[{0, 1, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 6]]; // _Wesley Ivan Hurt_, Jun 09 2016
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
|
