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A208466 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.

%I A208466 #8 Oct 14 2024 15:37:28
%S A208466 1,2,2,5,15,5,15,198,203,15,52,4041,20746,4140,52,203,113458,4132120,
%T A208466 4150760,115975,203,877,4132120,1358524513,10318694804,1366230232,
%U A208466 4213597,877,4140,187612143,671329819215,50996571454200,51074630353994
%N A208466 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 A208466 R. H. Hardin, <a href="/A208466/b208466.txt">Table of n, a(n) for n = 1..58</a>
%e A208466 Table starts:
%e A208466 ....1...........2..................5.....................15
%e A208466 ....2..........15................198...................4041
%e A208466 ....5.........203..............20746................4132120
%e A208466 ...15........4140............4150760............10318694804
%e A208466 ...52......115975.........1366230232.........51074630353994
%e A208466 ..203.....4213597.......675203938944.....441285917587055633
%e A208466 ..877...190899322....470798015742024.6105599904286957450405
%e A208466 .4140.10480142147.442649055938121520
%e A208466 Some solutions for n=4 and k=3:
%e A208466 ..0..1..2....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A208466 ..0..0..1....0..1..0....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0
%e A208466 ..0..0..0....0..0..2....2..0..0....2..0..1....1..1..0....0..2..0....0..0..0
%e A208466 ..0..1..0....0..0..0....0..2..0....0..0..0....0..0..0....0..0..0....0..2..1
%Y A208466 Column 1 and row 1 are A000110.
%Y A208466 Column 2 is A020557.
%K A208466 nonn,tabl
%O A208466 1,2
%A A208466 _R. H. Hardin_, Feb 27 2012