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A250686 Number of (n+1) X (3+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 A250686 #6 Aug 01 2023 17:43:52
%S A250686 2541,13906,74631,383440,1848953,8474002,37322413,159438246,665575403,
%T A250686 2731006288,11064772389,44421077632,177194842907,703795289106,
%U A250686 2787900969927,11027407758154,43593798115489,172349301152440
%N A250686 Number of (n+1) X (3+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 A250686 Column 3 of A250691.
%H A250686 R. H. Hardin, <a href="/A250686/b250686.txt">Table of n, a(n) for n = 1..210</a>
%F A250686 Empirical: a(n) = 27*a(n-1) -331*a(n-2) +2439*a(n-3) -12049*a(n-4) +42129*a(n-5) -107225*a(n-6) +201069*a(n-7) -277706*a(n-8) +278928*a(n-9) -197984*a(n-10) +94032*a(n-11) -26784*a(n-12) +3456*a(n-13) for n>17.
%e A250686 Some solutions for n=3
%e A250686 ..3..3..0..0....0..0..0..0....2..3..2..0....3..2..0..1....2..2..2..2
%e A250686 ..2..2..1..1....3..3..3..3....2..3..2..1....3..2..1..2....1..1..1..1
%e A250686 ..1..1..0..0....0..0..0..0....1..2..1..0....3..2..1..2....1..1..2..2
%e A250686 ..0..0..1..2....0..2..3..3....0..3..2..3....2..1..2..3....0..2..3..3
%Y A250686 Cf. A250691.
%K A250686 nonn
%O A250686 1,1
%A A250686 _R. H. Hardin_, Nov 26 2014