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 A047472 #22 Aug 31 2024 17:02:45
%S A047472 0,1,3,8,9,11,16,17,19,24,25,27,32,33,35,40,41,43,48,49,51,56,57,59,
%T A047472 64,65,67,72,73,75,80,81,83,88,89,91,96,97,99,104,105,107,112,113,115,
%U A047472 120,121,123,128,129,131,136,137,139,144,145,147,152,153,155
%N A047472 Numbers that are congruent to {0, 1, 3} (mod 8).
%H A047472 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047472 Equals partial sums of (0, 1, 2, 5, 1, 2, 5, 1, 2, 5, ...). - _Gary W. Adamson_, Jun 19 2008
%F A047472 From _Colin Barker_, Jan 26 2012: (Start)
%F A047472 G.f.: x^2*(1+2*x+5*x^2)/(1-x-x^3+x^4).
%F A047472 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. (End)
%F A047472 From _Wesley Ivan Hurt_, Jun 09 2016: (Start)
%F A047472 a(n) = 8*n/3 - 4 - cos(2*n*Pi/3) + 5*sin(2*n*Pi/3)/(3*sqrt(3)).
%F A047472 a(3k) = 8k-5, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)
%p A047472 A047472:=n->8*n/3-4-cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047472(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016
%t A047472 Select[Range[0, 150], MemberQ[{0, 1, 3}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)
%t A047472 LinearRecurrence[{1,0,1,-1},{0,1,3,8},60] (* _Harvey P. Dale_, Aug 31 2024 *)
%o A047472 (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 3]]; // _Wesley Ivan Hurt_, Jun 09 2016
%K A047472 nonn,easy
%O A047472 1,3
%A A047472 _N. J. A. Sloane_