%I #41 Sep 08 2022 08:44:57
%S 0,2,6,8,10,14,16,18,22,24,26,30,32,34,38,40,42,46,48,50,54,56,58,62,
%T 64,66,70,72,74,78,80,82,86,88,90,94,96,98,102,104,106,110,112,114,
%U 118,120,122,126,128,130,134,136,138,142,144,146,150,152,154,158
%N Numbers that are congruent to {0, 2, 6} mod 8.
%C The members of this sequence together with the members of A017113 give the even numbers. - _Wesley Ivan Hurt_, Apr 01 2014
%H Vincenzo Librandi, <a href="/A047395/b047395.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F From _R. J. Mathar_, Dec 05 2011: (Start)
%F G.f.: 2*x^2*(1+x)^2 / ((1+x+x^2)*(x-1)^2).
%F a(n) = 2 * A042965(n). (End)
%F From _Wesley Ivan Hurt_, Jun 13 2016: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F a(n) = 2*(12*n-12+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 8k-2, a(3k-1) = 8k-6, a(3k-2) = 8k-8. (End)
%F a(n) = 2*(n - 1 + floor(n/3)). - _Wolfdieter Lang_, Sep 11 2021
%F Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*log(sqrt(2)+2)/4 - (sqrt(2)-1)*log(2)/8. - _Amiram Eldar_, Dec 19 2021
%p A047395:=n->2*floor((4*n-3)/3); seq(A047395(n), n=1..100); # _Wesley Ivan Hurt_, Apr 01 2014
%t Table[2 Floor[(4 n - 3)/3], {n, 100}] (* _Wesley Ivan Hurt_, Apr 01 2014 *)
%t Flatten[Table[8n + {0, 2, 6}, {n, 0, 19}]] (* _Alonso del Arte_, Apr 11 2014 *)
%t LinearRecurrence[{1, 0, 1, -1}, {0, 2, 6, 8}, 100] (* _Vincenzo Librandi_, Jun 14 2016 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 6]]; // _Wesley Ivan Hurt_, Jun 13 2016
%Y Cf. A017113, A042965, A047407, A047410, A047464.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_