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

1,2

Links

Table of n, a(n) for n=1..45.

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

Cf. A347928, A319539, A088674.

Sequence in context: A193998 A209171 A368150 * A160855 A120232 A292961

Adjacent sequences: A348683 A348684 A348685 * A348687 A348688 A348689

Keyword

nonn,tabl

Author

Peter Luschny, Oct 29 2021

Status

approved