This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047464 #28 Aug 25 2025 10:40:17
%S A047464 0,2,4,8,10,12,16,18,20,24,26,28,32,34,36,40,42,44,48,50,52,56,58,60,
%T A047464 64,66,68,72,74,76,80,82,84,88,90,92,96,98,100,104,106,108,112,114,
%U A047464 116,120,122,124,128,130,132,136,138,140,144,146,148,152,154,156
%N A047464 Numbers that are congruent to {0, 2, 4} mod 8.
%H A047464 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047464 a(n) = 2*floor((n-1)/3)+2*n-2. - _Gary Detlefs_, Mar 18 2010
%F A047464 a(n) = 2*A004773(n-1). G.f.: 2*x^2*(1+x+2*x^2)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Mar 29 2010
%F A047464 From _Wesley Ivan Hurt_, Jun 10 2016: (Start)
%F A047464 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A047464 a(n) = 2*(12*n-15-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
%F A047464 a(3k) = 8k-4, a(3k-1) = 8k-6, a(3k-2) = 8k-8. (End)
%F A047464 Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + (2-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - _Amiram Eldar_, Dec 19 2021
%F A047464 a(n) = A047217(n)+n-1. - _R. J. Mathar_, Aug 25 2025
%p A047464 A047464:=n->2*(12*n-15-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047464(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016
%t A047464 Flatten[#+{0,2,4}&/@(8Range[0,20])] (* or *) LinearRecurrence[{1,0,1,-1}, {0,2,4,8}, 80] (* _Harvey P. Dale_, May 04 2013 *)
%o A047464 (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 4]]; // _Wesley Ivan Hurt_, Jun 10 2016
%Y A047464 Cf. A004773, A047395, A047407, A047410.
%K A047464 nonn,easy,changed
%O A047464 1,2
%A A047464 _N. J. A. Sloane_