1,12

Row sums are:

{0, 1, 1, 3, 4, 4, 21, 24, 25, 25, 651, 672, 675, 676, 676, 457653, 458304, 458325, 458328, 458329, 458329};

The roots of these polynomials are called Misiurewicz points and they are found in the antenna areas of the Mandelbrot set M.

Lennart Carleson and Theodore W. Gamelin, Complex Dynamics, Springer,New York,1993, page 133 ff

Pc(x,n)-> Nested ( z^2+x: when z->x): A137560; Pc(x,n)-Pc(x,m); n<>m;

{-1, 1},

{0, 0, 1},

{-1, 1, 1},

{0, 0, 0, 2, 1},

{0, 0, 1, 2, 1},

{-1, 1, 1, 2, 1},

{0, 0, 0, 0, 4, 6, 6, 4, 1},

{0, 0, 0, 2, 5, 6, 6, 4, 1},

{0, 0, 1, 2, 5, 6, 6, 4, 1},

{-1, 1, 1, 2, 5, 6, 6, 4, 1},

{0, 0, 0, 0, 0, 8, 20, 40, 68, 94, 114, 116, 94, 60, 28, 8, 1},

{0, 0, 0, 0, 4, 14, 26, 44, 69, 94, 114, 116, 94, 60, 28, 8, 1},

{0, 0, 0, 2,5, 14, 26, 44, 69, 94, 114, 116, 94, 60, 28, 8, 1},

{0, 0, 1, 2, 5, 14, 26, 44, 69, 94, 114, 116, 94, 60, 28, 8, 1},

{-1, 1, 1, 2, 5, 14, 26, 44, 69, 94, 114, 116, 94, 60, 28, 8, 1},

{0, 0, 0, 0, 0, 0, 16, 56, 152, 376, 844, 1744, 3340, 5976, 10040, 15856, 23460, 32398, 41658, 49700, 54746, 55308, 50788, 41944, 30782, 19788, 10948, 5096, 1932, 568, 120, 16, 1},

{0, 0, 0, 0, 0, 8, 36, 96, 220, 470, 958, 1860, 3434, 6036, 10068, 15864, 23461, 32398, 41658, 49700, 54746, 55308, 50788, 41944, 30782, 19788, 10948, 5096, 1932, 568, 120, 16, 1},

{0, 0, 0, 0, 4, 14, 42, 100, 221, 470, 958, 1860, 3434, 6036, 10068, 15864, 23461, 32398, 41658, 49700, 54746, 55308, 50788, 41944, 30782, 19788, 10948, 5096, 1932, 568, 120, 16, 1},

{0, 0, 0, 2, 5, 14, 42, 100, 221, 470, 958, 1860, 3434, 6036, 10068, 15864, 23461, 32398, 41658, 49700, 54746, 55308, 50788, 41944, 30782, 19788, 10948, 5096, 1932, 568, 120, 16, 1},

{0, 0, 1, 2, 5, 14, 42, 100, 221, 470, 958, 1860, 3434, 6036, 10068, 15864, 23461, 32398, 41658, 49700, 54746, 55308, 50788, 41944, 30782, 19788, 10948, 5096, 1932, 568, 120, 16, 1},

{-1, 1, 1, 2, 5, 14, 42, 100, 221, 470, 958, 1860, 3434, 6036, 10068, 15864, 23461, 32398, 41658, 49700, 54746, 55308, 50788, 41944, 30782, 19788, 10948, 5096, 1932, 568, 120, 16, 1}

Clear[f, g, h, x]; f[z_] = z^2 + x; g = Join[{1}, ExpandAll[NestList[f, x, 5]]]; h = Union[Flatten[Table[Flatten[Table[If[n == m, {}, ExpandAll[g[[ n]] - g[[m]]]], {m, 1, n}]], {n, 1, Length[g]}]]]; a = Table[CoefficientList[h[[n]], x], {n, 1, Length[h]}]; Flatten[a] Table[Apply[Plus, CoefficientList[h[[n]], x]], {n, 1, Length[h]}];

Sequence in context: A029409 A014674 A015339 this_sequence A111143 A004197 A048571

Adjacent sequences: A137864 A137865 A137866 this_sequence A137868 A137869 A137870

tabl,uned,sign

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 29 2008