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%I #6 Jan 11 2015 11:07:05
%S 28107,305707,1636717,5195288,10966149,19685575,33767784,53908650,
%T 79636678,111887770,154273666,208551891,273063404,349350730,443497974,
%U 557840034,689156599,839938280,1019433332,1230639389,1468352504
%N Number of (5+1)X(n+1) 0..2 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically
%C Row 5 of A253749
%H R. H. Hardin, <a href="/A253753/b253753.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +4*a(n-4) -12*a(n-5) +12*a(n-6) -4*a(n-7) -6*a(n-8) +18*a(n-9) -18*a(n-10) +6*a(n-11) +4*a(n-12) -12*a(n-13) +12*a(n-14) -4*a(n-15) -a(n-16) +3*a(n-17) -3*a(n-18) +a(n-19) for n>28
%F Empirical for n mod 4 = 0: a(n) = (319/768)*n^6 + (357227/7680)*n^5 + (182225/64)*n^4 + (22602713/384)*n^3 + (2800411/6)*n^2 - (128547201/40)*n + 6338652 for n>9
%F Empirical for n mod 4 = 1: a(n) = (319/768)*n^6 + (357227/7680)*n^5 + (182225/64)*n^4 + (15060613/256)*n^3 + (357971639/768)*n^2 - (24773998217/7680)*n + (816584243/128) for n>9
%F Empirical for n mod 4 = 2: a(n) = (319/768)*n^6 + (357227/7680)*n^5 + (182225/64)*n^4 + (22559891/384)*n^3 + (88566155/192)*n^2 - (265291527/80)*n + (106109999/16) for n>9
%F Empirical for n mod 4 = 3: a(n) = (319/768)*n^6 + (357227/7680)*n^5 + (182225/64)*n^4 + (15047617/256)*n^3 + (354548051/768)*n^2 - (25372897937/7680)*n + (845522525/128) for n>9
%e Some solutions for n=1
%e ..0..1....0..2....0..1....1..1....0..1....0..0....0..0....0..0....0..0....0..1
%e ..0..0....1..1....0..1....0..0....0..1....2..1....0..0....0..1....2..1....1..0
%e ..2..0....0..1....0..1....0..2....1..1....2..1....0..0....0..1....2..0....0..0
%e ..2..1....1..2....1..1....2..2....2..1....1..1....0..1....0..1....1..1....1..1
%e ..2..1....1..1....0..1....0..0....2..0....1..2....2..1....0..2....2..2....0..0
%e ..1..2....0..2....0..2....2..2....2..1....0..2....2..1....2..2....2..2....1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 11 2015
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