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%I #8 Aug 19 2022 15:11:46
%S 7803,75959,382973,1143174,2351928,4249381,7348144,11783014,17227486,
%T 24218260,33845194,46241656,60632621,78042368,100341383,127587830,
%U 158431665,194599303,238993938,291534619,350130482,417457176,497739626
%N Number of (4+1) X (n+1) 0..2 arrays with every 2 X 2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically.
%C Row 4 of A253749.
%H R. H. Hardin, <a href="/A253752/b253752.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>27.
%F Empirical for n mod 4 = 0: a(n) = (4873/23040)*n^6 + (241919/15360)*n^5 + (3034139/4608)*n^4 + (4726559/384)*n^3 + (7406437/90)*n^2 - (15218987/30)*n + 1005182 for n>8.
%F Empirical for n mod 4 = 1: a(n) = (4873/23040)*n^6 + (241919/15360)*n^5 + (3034139/4608)*n^4 + (18843205/1536)*n^3 + (1878126757/23040)*n^2 - (2674526163/5120)*n + (522413747/512) for n>8.
%F Empirical for n mod 4 = 2: a(n) = (4873/23040)*n^6 + (241919/15360)*n^5 + (3034139/4608)*n^4 + (146755/12)*n^3 + (14433929/180)*n^2 - (525506959/960)*n + (34331513/32) for n>8.
%F Empirical for n mod 4 = 3: a(n) = (4873/23040)*n^6 + (241919/15360)*n^5 + (3034139/4608)*n^4 + (18844129/1536)*n^3 + (1862199637/23040)*n^2 - (2736248123/5120)*n + (544432283/512) for n>8.
%e Some solutions for n=2
%e ..2..0..0....0..0..2....1..0..1....0..1..2....0..0..2....1..0..0....1..0..0
%e ..1..0..0....0..0..0....2..0..2....2..1..0....0..0..1....1..0..0....1..0..2
%e ..1..1..1....2..0..0....1..0..2....2..1..2....0..0..1....2..0..1....2..1..2
%e ..2..1..1....2..0..1....2..1..2....1..1..2....2..2..1....2..1..1....2..1..2
%e ..2..0..1....2..2..1....0..1..2....1..2..2....2..0..0....2..2..0....1..1..2
%Y Cf. A253749.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 11 2015
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