OFFSET
1,12
COMMENTS
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.
REFERENCES
Lennart Carleson and Theodore W. Gamelin, Complex Dynamics, Springer, New York, 1993, p. 133ff.
FORMULA
Pc(x,n)-> Nested ( z^2+x: when z->x): A137560; Pc(x,n)-Pc(x,m); n<>m;
EXAMPLE
{-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}
MATHEMATICA
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]}];
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Apr 29 2008
STATUS
approved