|
%I #21 Apr 04 2024 10:55:41
%S 0,0,0,1,69,3072,122833,4915726,204051186,8849413857,399736867216,
%T 18698541563923,900653139548828,44458651801451163,2240500172425946056,
%U 114922424191743943701,5985232324581998309113,315879022416448194306768
%N Number of n X n nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.
%C Diagonal of A253004.
%H Robert Dougherty-Bliss and Manuel Kauers, <a href="/A252998/b252998.txt">Table of n, a(n) for n = 1..101</a> (first 24 terms by R. H. Hardin).
%H Robert Dougherty-Bliss, <a href="https://sites.math.rutgers.edu/~zeilberg/Theses/RobertDoughertyBlissThesis.pdf">Experimental Methods in Number Theory and Combinatorics</a>, Ph. D. Dissertation, Rutgers Univ. (2024). See p. 29.
%H Robert Dougherty-Bliss and Manuel Kauers, <a href="https://arxiv.org/abs/2309.00487">Hardinian Arrays</a>, arXiv:2309.00487 [math.CO], 2023.
%H Robert Dougherty-Bliss and Manuel Kauers, <a href="/A252998/a252998.txt">Conjectured recurrence of order 9</a>
%e Some solutions for n=6:
%e ..0..0..1..1..1..2....0..0..1..1..1..2....0..1..1..1..2..2....0..0..1..1..1..2
%e ..0..0..1..1..1..2....0..1..1..1..2..2....1..1..1..1..2..2....0..1..1..1..1..2
%e ..1..1..1..1..1..2....0..1..1..2..2..2....1..1..1..2..2..2....0..1..1..2..2..2
%e ..1..1..2..2..2..2....1..1..1..2..2..2....2..2..2..2..2..2....1..1..1..2..2..2
%e ..1..2..2..2..2..2....1..1..1..2..2..2....2..2..2..2..2..2....1..2..2..2..2..2
%e ..2..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2
%Y Cf. A253004.
%K nonn
%O 1,5
%A _R. H. Hardin_, Dec 25 2014
| 