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A250913 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having its maximum diagonal element less than its minimum antidiagonal element.

%I A250913 #6 Jul 23 2025 12:50:58
%S A250913 74,603,603,4909,13401,4909,39960,297873,297873,39960,325277,6621219,
%T A250913 18077319,6621219,325277,2647773,147178899,1096982379,1096982379,
%U A250913 147178899,2647773,21553018,3271547025,66566704705,181725094746
%N A250913 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having its maximum diagonal element less than its minimum antidiagonal element.
%C A250913 Table starts
%C A250913 .......74.........603............4909..............39960.................325277
%C A250913 ......603.......13401..........297873............6621219..............147178899
%C A250913 .....4909......297873........18077319.........1096982379............66566704705
%C A250913 ....39960.....6621219......1096982379.......181725094746.........30104106257115
%C A250913 ...325277...147178899.....66566704705.....30104106257115......13614176466285177
%C A250913 ..2647773..3271547025...4039362762435...4986961280614953....6156816533805174849
%C A250913 .21553018.72721157625.245114118899485.826125782084148708.2784331051704024117237
%H A250913 R. H. Hardin, <a href="/A250913/b250913.txt">Table of n, a(n) for n = 1..220</a>
%F A250913 Empirical for column k:
%F A250913 k=1: a(n) = 9*a(n-1) -7*a(n-2)
%F A250913 k=2: a(n) = 24*a(n-1) -41*a(n-2) +36*a(n-3)
%F A250913 k=3: [order 7]
%F A250913 k=4: [order 13]
%F A250913 k=5: [order 30]
%e A250913 Some solutions for n=2 k=4
%e A250913 ..0..1..2..1..1....0..1..1..0..1....0..1..2..1..0....0..0..2..1..1
%e A250913 ..0..0..2..1..2....0..0..0..2..2....0..0..1..1..2....0..0..1..1..2
%e A250913 ..1..0..1..0..0....0..0..0..0..1....0..1..2..1..1....0..0..2..0..2
%Y A250913 Column 1 is A190984(n+2)
%K A250913 nonn,tabl
%O A250913 1,1
%A A250913 _R. H. Hardin_, Nov 28 2014