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A250540 Number of (n+1) X (4+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.

%I A250540 #6 Jun 26 2025 12:36:38
%S A250540 36552,491650,4169584,27240292,151170400,752602024,3475227442,
%T A250540 15210145612,64036997144,262068107390,1050500245716,4148232147580,
%U A250540 16207817815736,62874459765364,242824935032646,935658630855012
%N A250540 Number of (n+1) X (4+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.
%C A250540 Column 4 of A250544.
%H A250540 R. H. Hardin, <a href="/A250540/b250540.txt">Table of n, a(n) for n = 1..210</a>
%F A250540 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 A250540 Some solutions for n=1
%e A250540 ..2..3..0..1..1....0..2..0..0..0....3..1..2..0..2....3..1..2..2..0
%e A250540 ..1..2..0..3..3....0..2..0..3..3....0..0..2..0..3....0..1..2..2..2
%Y A250540 Cf. A250544.
%K A250540 nonn
%O A250540 1,1
%A A250540 _R. H. Hardin_, Nov 24 2014