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%I #8 Dec 16 2018 06:44:47
%S 414,1377,3090,5386,9679,20975,51167,133311,362399,1014975,2903327,
%T 8429631,24731039,73080255,217017887,646610751,1930949279,5775084735,
%U 17289730847,51798148671,155252361119,465472916415,1395850418207
%N Number of (2+1) X (n+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
%H R. H. Hardin, <a href="/A253496/b253496.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>9.
%F Empirical: a(n) = 400*3^(n-3) + 271*2^(n-1) + 1423 for n>6.
%F Empirical g.f.: x*(414 - 1107*x - 618*x^2 - 491*x^3 + 3091*x^4 + 3607*x^5 - 530*x^6 - 1040*x^7 - 480*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Dec 16 2018
%e Some solutions for n=4:
%e ..0..1..1..0..1....0..2..2..1..1....0..2..2..1..1....1..0..2..0..0
%e ..2..2..1..0..1....2..2..1..0..0....2..1..1..0..0....1..0..2..0..0
%e ..0..0..0..0..2....2..2..1..0..0....2..1..1..0..1....1..0..2..0..0
%Y Row 2 of A253495.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 02 2015
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