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%I #8 Dec 16 2018 07:12:01
%S 1388,2640,4196,6476,11937,25715,60586,151946,399466,1088906,3050986,
%T 8724746,25321066,74260106,219377386,651329546,1940386666,5793959306,
%U 17327479786,51873646346,155403356266,465774906506,1396454398186
%N Number of (3+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="/A253497/b253497.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) + 415*2^(n-1) + 1626 for n>6.
%F Empirical g.f.: x*(1388 - 5688*x + 3624*x^2 + 2012*x^3 + 3397*x^4 + 153*x^5 - 1253*x^6 - 327*x^7 - 54*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..2..2....0..2..2..1..1....0..1..1..1..1....0..1..2..2..2
%e ..2..2..1..1..0....1..1..1..0..0....1..1..0..0..0....1..1..1..1..1
%e ..2..2..1..1..0....1..1..1..0..0....2..1..0..0..0....2..2..2..2..2
%e ..0..0..0..1..2....0..0..0..0..1....2..1..0..0..2....1..1..1..1..1
%Y Row 3 of A253495.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 02 2015
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