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 A137719 #32 Dec 31 2023 10:24:56
%S A137719 0,2,1,2,3,3,3,5,4,5,6,6,6,8,7,8,9,9,9,11,10,11,12,12,12,14,13,14,15,
%T A137719 15,15,17,16,17,18,18,18,20,19,20,21,21,21,23,22,23,24,24,24,26,25,26,
%U A137719 27,27,27,29,28,29,30,30,30,32,31,32,33,33,33,35,34
%N A137719 Sequence based on the pattern [3n, 3n, 3n, 3n+2, 3n+1, 3n+2].
%C A137719 Powers of 2 in a scaled version of the Hankel transform of A106191.
%H A137719 M. F. Hasler, <a href="/A137719/b137719.txt">Table of n, a(n) for n = 0..1000</a>
%H A137719 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1).
%F A137719 a(n) = log(abs(A137718(n)))/log(2).
%F A137719 From _R. J. Mathar_, Feb 10 2008: (Start)
%F A137719 O.g.f.: 1/(2*(x-1)^2) + (x-1)/(3*(x^2+x+1)) - 1/(4*(x+1)) - 1/(12*(x-1)).
%F A137719 a(n) = 3 + a(n-6). (End)
%F A137719 From _Colin Barker_, Jun 27 2013: (Start)
%F A137719 a(n) = a(n-2) + a(n-3) - a(n-5).
%F A137719 G.f.: x*(x+2) / ((x-1)^2*(x+1)*(x^2+x+1)). (End)
%F A137719 a(n) = Sum_{i=0..floor(n/2)} (2n-i mod 3). - _Wesley Ivan Hurt_, Mar 22 2016
%F A137719 a(n) = A004526(n+1) + A079978(n). - _R. J. Mathar_, Oct 27 2019
%p A137719 A137719:=n->add(2*n-i mod 3, i=0..floor(n/2)): seq(A137719(n), n=0..100); # _Wesley Ivan Hurt_, Mar 21 2016
%t A137719 Table[Sum[Mod[2 n - i, 3], {i, 0, Floor[n/2]}], {n, 0, 80}] (* _Wesley Ivan Hurt_, Mar 21 2016 *)
%o A137719 (Magma) [&+[(2*n-i) mod 3: i in [0..Floor(n/2)]]: n in [0..80]]; // _Wesley Ivan Hurt_, Mar 21 2016
%o A137719 (PARI) apply( A137719(n)={(n=divrem(n-1,6))[1]*3+min(n[2]+2*!n[2],3)}, [0..30]) \\ _M. F. Hasler_, Oct 27 2019
%Y A137719 Cf. A106191, A137718.
%K A137719 easy,nonn
%O A137719 0,2
%A A137719 _Paul Barry_, Feb 08 2008