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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
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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.
EXAMPLE
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;
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;
CROSSREFS
Sequence in context: A193998 A209171 A368150 * A160855 A120232 A292961
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Oct 29 2021
STATUS
approved

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Last modified June 17 00:51 EDT 2024. Contains 373432 sequences. (Running on oeis4.)