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 A242364 #4 Jun 12 2014 21:12:29
%S A242364 1,0,2,-1,4,-3,-2,3,8,-7,-6,-4,5,6,16,-15,-14,-12,-8,-5,7,9,10,12,32,
%T A242364 -31,-30,-28,-24,-16,-11,-10,-9,13,14,15,17,18,20,24,64,-63,-62,-60,
%U A242364 -56,-48,-32,-23,-22,-20,-19,-18,-17,-13,11,25,26,28,29,30,31
%N A242364 Irregular triangular array of all the integers ordered as in Comments.
%C A242364 Let f1(x) = 2x, f2(x) = 1-x, f3(x) = 2-x, g(1) = (1), and g(n) = union(f1(g(n-1)), f2(g(n-1)),f3(g(n-1))) for n >1. Let T be the array whose n-th row consists of the numbers in g(n) arranged in increasing order. It is easy to prove that every integer occurs exactly once in T. Conjectures: (1) |g(n)| = 2*F(n-1) for n >=2, where F = A000045 (the Fibonacci numbers), and exactly half of the numbers in g(n) are positive; (2) the number of even numbers in g(n) is 2*F(n-2) and the number of odd numbers is 2*F(n-3).
%H A242364 Clark Kimberling, <a href="/A242364/b242364.txt">Table of n, a(n) for n = 1..3000</a>
%e A242364 First 6 rows of the array:
%e A242364 1
%e A242364 0 .... 2
%e A242364 -1 ... 4
%e A242364 -3 ... -2 .... 3 .... 8
%e A242364 -7 ... -6 ... -4 .... 5 .... 6 .... 16
%e A242364 -15 .. -14 .. -12 .. -8 .... -5 ... 7 ... 9 ... 10 ... 12 ... 32
%t A242364 z = 12; g[1] = {1}; f1[x_] := 2 x; f2[x_] := 1 - x; f3[x_] := 2 - x; h[1] = g[1]; b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]], f3[g[n - 1]]]]; h[n_] := h[n] = Union[h[n - 1], g[n - 1]]; g[n_] := g[n] = Complement [b[n], Intersection[b[n], h[n]]]; u = Table[g[n], {n, 1, 9}]
%t A242364 u1 = Flatten[u] (* A242364 *)
%t A242364 v = Table[Reverse[Drop[g[n], Fibonacci[n - 1]]], {n, 1, z}]
%t A242364 v1 = Flatten[v] (* A242365 *)
%t A242364 w1 = Table[Apply[Plus, g[n]], {n, 1, 20}] (* A243735 *)
%t A242364 w2 = Table[Apply[Plus, v[[n]]], {n, 1, 10}] (* A243736 *)
%Y A242364 Cf. A242365, A243735, A243736, A242448, A000045.
%K A242364 easy,tabf,sign
%O A242364 1,3
%A A242364 _Clark Kimberling_, Jun 11 2014