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 A194272 #34 Sep 08 2022 08:45:58
%S A194272 1,2,3,3,3,3,4,5,6,6,6,6,7,8,9,9,9,9,10,11,12,12,12,12,13,14,15,15,15,
%T A194272 15,16,17,18,18,18,18,19,20,21,21,21,21,22,23,24,24,24,24,25,26,27,27,
%U A194272 27,27,28,29,30,30,30,30,31,32,33,33,33,33,34,35,36,36,36,36
%N A194272 Array T(n,k) with 6 columns read by rows in which row n lists 3*n-2, 3*n-1, 3*n, 3*n, 3*n, 3*n.
%C A194272 Also first differences of A194273 which is also a sequence related to cellular automata.
%H A194272 G. C. Greubel, <a href="/A194272/b194272.txt">Table of n, a(n) for n = 1..10000</a>
%H A194272 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A194272 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,-1,2,-1).
%F A194272 From _Michael Somos_, May 12 2014: (Start)
%F A194272 Euler transform of length 6 sequence [2, 0, -1, 0, 0, 1].
%F A194272 G.f.: x * (1-x^3) / ( (1-x)^2 * (1-x^6) ).
%F A194272 a(n-1) = A047926(n) - A132868(n). (End)
%F A194272 From _Wesley Ivan Hurt_, Apr 04 2015, Sep 08 2015: (Start)
%F A194272 a(n) = 2*a(n-1)-a(n-2)-a(n-3)+2*a(n-4)-a(n-5), n>5.
%F A194272 a(n) = floor((n+3)/6) + floor((n+4)/6) + floor((n+5)/6).
%F A194272 a(n) = Sum_{i=0..n-1} floor(i/6) - floor((i-3)/6). (End)
%e A194272 Array begins:
%e A194272 1, 2, 3, 3, 3, 3,
%e A194272 4, 5, 6, 6, 6, 6,
%e A194272 7, 8, 9, 9, 9, 9,
%e A194272 10, 11, 12, 12, 12, 12,
%e A194272 13, 14, 15, 15, 15, 15,
%e A194272 16, 17, 18, 18, 18, 18,
%e A194272 19, 20, 21, 21, 21, 21,
%e A194272 22, 23, 24, 24, 24, 24,
%e A194272 ...
%e A194272 Sum of row n gives 18*n-3 = A008600(n) - 3.
%e A194272 G.f. = x + 2*x^2 + 3*x^3 + 3*x^4 + 3*x^5 + 3*x^6 + 4*x^7 + 5*x^8 + ...
%p A194272 A194272:=n->floor((n+3)/6) + floor((n+4)/6) + floor((n+5)/6): seq(A194272(n), n=1..100); # _Wesley Ivan Hurt_, Apr 04 2015
%t A194272 Table[Floor[(n + 3)/6] + Floor[(n + 4)/6] + Floor[(n + 5)/6], {n, 100}] (* _Wesley Ivan Hurt_, Apr 04 2015 *)
%o A194272 (Magma) [Floor((n+3)/6) + Floor((n+4)/6) + Floor((n+5)/6) : n in [1..100]]; // _Wesley Ivan Hurt_, Apr 04 2015
%o A194272 (PARI) x='x+O('x^60); Vec(x*(1-x^3)/((1-x)^2*(1-x^6))) \\ _G. C. Greubel_, Aug 13 2018
%Y A194272 Column 1: A016777. Column 2: A016789. Every column 3, 4, 5 and 6: positive integers of A008585.
%Y A194272 Cf. A008600, A047926, A132868, A194273.
%K A194272 nonn,easy,tabf
%O A194272 1,2
%A A194272 _Omar E. Pol_, Aug 20 2011