A348686 Array read by ascending antidiagonals: T(n, k) = P(n, k) where P(n, x) are the scaled Mandelbrot-Larsen polynomials defined in A347928.
1, 3, 2, 6, 8, 3, 45, 32, 15, 4, 126, 256, 90, 24, 5, 750, 1536, 885, 192, 35, 6, 2796, 12288, 8010, 2304, 350, 48, 7, 19389, 90112, 85590, 27648, 5005, 576, 63, 8, 75894, 753664, 913140, 374784, 74550, 9600, 882, 80, 9
Offset: 1
Examples
Array starts: [1] 1, 2, 3, 4, 5, 6, 7, ... [2] 3, 8, 15, 24, 35, 48, 63, ... [3] 6, 32, 90, 192, 350, 576, 882, ... [4] 45, 256, 885, 2304, 5005, 9600, 16821, ... [5] 126, 1536, 8010, 27648, 74550, 170496, 346626, ... [6] 750, 12288, 85590, 374784, 1229550, 3317760, 7778358, ... [7] 2796, 90112, 913140, 5210112, 21017500, 67239936, 182244132, ... [8] 19389, 753664, 10384845, 75890688, 374119165, 1415184384, 4428038349, ... Seen as a triangle: [1] 1; [2] 3, 2; [3] 6, 8, 3; [4] 45, 32, 15, 4; [5] 126, 256, 90, 24, 5; [6] 750, 1536, 885, 192, 35, 6; [7] 2796, 12288, 8010, 2304, 350, 48, 7; [8] 19389, 90112, 85590, 27648, 5005, 576, 63, 8; [9] 75894, 753664, 913140, 374784, 74550, 9600, 882, 80, 9;
Links
- Neil J. Calkin, Eunice Y. S. Chan, and Robert M. Corless, Some Facts and Conjectures about Mandelbrot Polynomials, Maple Trans., Vol. 1, No. 1, Article 14037 (July 2021).
- Michael Larsen, Multiplicative series, modular forms, and Mandelbrot polynomials, in: Mathematics of Computation 90.327 (Sept. 2020), pp. 345-377. Preprint: arXiv:1908.09974 [math.NT], 2019.
Programs
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Maple
# Polynomials M are defined in A347928. P := (n, x) -> 2^(2*n-1)*M(n, x): row := (n, len) -> seq(P(n, k), k = 1..len): for n from 1 to 8 do row(n, 8) od;