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 A138061 #2 Mar 30 2012 17:34:26
%S A138061 2,2,6,2,6,12,2,6,12,4,2,6,12,4,5,12,2,6,12,4,5,12,7,16,27,2,6,12,4,5,
%T A138061 12,7,16,27,10,22,36,52,2,6,12,4,5,12,7,16,27,10,22,36,52,14,30,48,68,
%U A138061 18,2,6,12,4,5,12,7,16,27,10,22,36,52,14,30,48,68,18,19,40,63,88,23,24
%N A138061 This sequence is a triangular sequence formed by the substitution: ( French sideways graph) 1->1,2;2->3;3->4;4->1; as a Markov style substitution form. The result is the differential polynomial coefficient form. ( first zero omitted).
%C A138061 Row sums are:
%C A138061 {0, 2, 8, 20, 24, 41, 91, 211, 389, 696, 1307}
%C A138061 This uses the French sideways graph method as in:
%C A138061 A103684:the morphism f: 1->{1,2}, 2->{1,3}, 3->{3}.
%C A138061 These sequences in the polynomial form were created to see what the
%C A138061 fractal implicit pictures would look like and not for the sequences:
%C A138061 Clear[a, s, p, t, m, n, t, p, k]
%C A138061 (* substitution *)
%C A138061 s[1] = {1, 2}; s[2] = {3}; s[3] = {4}; s[4] = {1};
%C A138061 t[a_] := Flatten[s /(AT) a];
%C A138061 p[0] = {1}; p[1] = t[p[0]];
%C A138061 p[n_] := t[p[n - 1]];
%C A138061 a = Table[p[n], {n, 0, 12}];
%C A138061 k = Table[D[Apply[Plus, Table[
%C A138061 a[[n]][[m]]*x^(m - 1), {m, 1, Length[a[[n]]]}]], x], {n, 3, 13}];
%C A138061 Clear[x, y, a, b, f, z, p];
%C A138061 nr = k /. x -> z;
%C A138061 p[z_] = Apply[Times, nr];
%C A138061 z = x + I*y;
%C A138061 f[x_, y_] = Re[1/(p[z])];
%C A138061 ContourPlot[ f[x, y], {x, -1.61,1.61}, {y, -1.61, 1.61}, PlotPoints -> {300, 300}, ImageSize ->600, ColorFunction -> (Hue[2# ] &)]
%F A138061 ( French sideways graph) 1->1,2;2->3;3->4;4->1; Substitution->p(x,n); out_n,m=Coefficients(dp(x,n)/dx).
%e A138061 First zero omitted:
%e A138061 {2},
%e A138061 {2, 6},
%e A138061 {2, 6, 12},
%e A138061 {2, 6, 12, 4},
%e A138061 {2, 6, 12, 4, 5, 12},
%e A138061 {2, 6, 12, 4, 5, 12, 7, 16, 27},
%e A138061 {2, 6, 12, 4, 5, 12, 7, 16, 27, 10, 22, 36, 52},
%e A138061 {2, 6, 12, 4, 5, 12, 7, 16, 27, 10, 22, 36, 52, 14, 30, 48, 68, 18},
%e A138061 {2, 6, 12, 4, 5, 12, 7, 16, 27, 10, 22, 36, 52, 14, 30, 48, 68, 18, 19, 40, 63, 88, 23, 24, 50},
%e A138061 {2, 6, 12, 4, 5, 12, 7, 16, 27, 10, 22, 36, 52, 14, 30, 48, 68, 18, 19, 40, 63, 88, 23, 24, 50, 26, 54, 84, 116, 30, 31, 64, 33, 68, 105}
%t A138061 Clear[a, s, p, t, m, n] (* substitution *) s[1] = {1, 2}; s[2] = {3}; s[3] = {4}; s[4] = {1}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; a = Table[p[n], {n, 0, 10}]; Flatten[a]; b = Table[CoefficientList[D[Apply[Plus, Table[a[[n]][[m]]*x^(m - 1), {m, 1, Length[a[[n]]]}]], x], x], {n, 1, 11}]; Flatten[b] Table[Apply[Plus, CoefficientList[D[Apply[Plus, Table[a[[n]][[m]]*x^(m - 1), {m, 1, Length[a[[n]]]}]], x], x]], {n, 1, 11}];
%Y A138061 Cf. A103684.
%K A138061 nonn,uned,tabf
%O A138061 1,1
%A A138061 _Roger L. Bagula_, May 02 2008