%I #8 Oct 14 2024 15:37:28
%S 1,2,2,5,15,5,15,198,203,15,52,4041,20746,4140,52,203,113458,4132120,
%T 4150760,115975,203,877,4132120,1358524513,10318694804,1366230232,
%U 4213597,877,4140,187612143,671329819215,50996571454200,51074630353994
%N T(n,k) is the number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
%H R. H. Hardin, <a href="/A208466/b208466.txt">Table of n, a(n) for n = 1..58</a>
%e Table starts:
%e ....1...........2..................5.....................15
%e ....2..........15................198...................4041
%e ....5.........203..............20746................4132120
%e ...15........4140............4150760............10318694804
%e ...52......115975.........1366230232.........51074630353994
%e ..203.....4213597.......675203938944.....441285917587055633
%e ..877...190899322....470798015742024.6105599904286957450405
%e .4140.10480142147.442649055938121520
%e Some solutions for n=4 and k=3:
%e ..0..1..2....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e ..0..0..1....0..1..0....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0
%e ..0..0..0....0..0..2....2..0..0....2..0..1....1..1..0....0..2..0....0..0..0
%e ..0..1..0....0..0..0....0..2..0....0..0..0....0..0..0....0..0..0....0..2..1
%Y Column 1 and row 1 are A000110.
%Y Column 2 is A020557.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 27 2012