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A250698 Number of (7+1)X(n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

%I A250698 #6 Jul 23 2025 12:42:44
%S A250698 1005121,7249825,37322413,160222342,617657415,2224688673,7662909389,
%T A250698 25622390948,84040600357,272488719033,878393149045,2826884204762,
%U A250698 9107833801683,29426182298097,95415082577317,310574007541112
%N A250698 Number of (7+1)X(n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
%C A250698 Row 7 of A250691
%H A250698 R. H. Hardin, <a href="/A250698/b250698.txt">Table of n, a(n) for n = 1..22</a>
%F A250698 Empirical: a(n) = 30*a(n-1) -415*a(n-2) +3514*a(n-3) -20386*a(n-4) +85924*a(n-5) -272198*a(n-6) +661180*a(n-7) -1244717*a(n-8) +1822478*a(n-9) -2068955*a(n-10) +1802474*a(n-11) -1181760*a(n-12) +563888*a(n-13) -184752*a(n-14) +37152*a(n-15) -3456*a(n-16)
%e A250698 Some solutions for n=1
%e A250698 ..2..2....2..1....0..0....0..1....0..1....2..0....0..0....0..0....2..0....2..0
%e A250698 ..0..0....2..1....0..0....2..3....0..1....2..2....2..2....2..2....2..0....2..1
%e A250698 ..0..0....2..2....1..2....1..2....0..1....2..2....3..3....2..2....2..0....2..2
%e A250698 ..2..2....2..2....0..1....2..3....2..3....1..1....2..2....3..3....3..2....3..3
%e A250698 ..1..1....1..1....0..1....0..1....0..1....1..1....0..0....2..2....1..0....1..1
%e A250698 ..0..0....2..2....2..3....0..2....1..3....1..1....0..1....0..0....2..1....1..3
%e A250698 ..2..3....2..3....1..2....0..2....0..2....1..1....0..1....1..1....2..1....0..2
%e A250698 ..0..1....0..1....1..3....1..3....0..2....0..0....0..3....0..2....2..1....1..3
%K A250698 nonn
%O A250698 1,1
%A A250698 _R. H. Hardin_, Nov 26 2014