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Number of n X n nonnegative integer arrays with each row and column increasing from zero by 0 or 1.
1

%I #17 Mar 09 2024 11:03:43

%S 1,2,8,62,924,26394,1442764,150786848,30114993376,11489639088218,

%T 8372083277093216,11649087077771471438,30947648445392475219812,

%U 156963868041535457457609234,1519762800266538697863301357568

%N Number of n X n nonnegative integer arrays with each row and column increasing from zero by 0 or 1.

%H R. H. Hardin, <a href="/A202751/b202751.txt">Table of n, a(n) for n = 1..18</a>

%H Dylan Heuer, <a href="https://arxiv.org/abs/2403.02242">Partial Alternating Sign Matrix Bijections and Dynamics</a>, arXiv:2403.02242 [math.CO], 2024. See p. 6.

%H Dylan Heuer and Jessica Striker, <a href="https://arxiv.org/abs/2012.09901">Partial permutation and alternating sign matrix polytopes</a>, arXiv:2012.09901 [math.CO], 2020.

%e Some solutions for n=5:

%e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

%e 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0

%e 0 0 0 1 1 0 0 1 1 2 0 0 1 1 1 0 0 0 1 1

%e 0 1 1 1 1 0 0 1 2 3 0 1 1 2 2 0 0 1 2 2

%e 0 1 2 2 2 0 1 2 3 4 0 1 2 2 3 0 1 1 2 3

%Y Diagonal of A202756.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 23 2011