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A251228 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

%I A251228 #6 Jul 23 2025 13:11:54
%S A251228 14,49,49,171,305,171,597,1892,1892,597,2084,11753,20782,11753,2084,
%T A251228 7275,72985,228689,228689,72985,7275,25396,453273,2515011,4462968,
%U A251228 2515011,453273,25396,88654,2814985,27662994,87024544,87024544,27662994,2814985
%N A251228 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.
%C A251228 Table starts
%C A251228 ....14.......49........171..........597............2084..............7275
%C A251228 ....49......305.......1892........11753...........72985............453273
%C A251228 ...171.....1892......20782.......228689.........2515011..........27662994
%C A251228 ...597....11753.....228689......4462968........87024544........1697323707
%C A251228 ..2084....72985....2515011.....87024544......3007738372......103986727042
%C A251228 ..7275...453273...27662994...1697323707....103986727042.....6373427948731
%C A251228 .25396..2814985..304255924..33102432698...3594807908974...390586327228567
%C A251228 .88654.17482154.3346446223.645599385182.124275144041759.23937316421928928
%H A251228 R. H. Hardin, <a href="/A251228/b251228.txt">Table of n, a(n) for n = 1..449</a>
%F A251228 Empirical for column k:
%F A251228 k=1: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3)
%F A251228 k=2: a(n) = 5*a(n-1) +9*a(n-2) -8*a(n-3) -8*a(n-4) +3*a(n-5)
%F A251228 k=3: [order 8]
%F A251228 k=4: [order 17]
%F A251228 k=5: [order 29]
%F A251228 k=6: [order 54] for n>55
%F A251228 k=7: [order 99] for n>101
%e A251228 Some solutions for n=3 k=4
%e A251228 ..0..0..0..0..1....0..0..0..1..0....0..0..1..0..1....0..0..0..1..1
%e A251228 ..1..0..0..1..0....0..1..1..0..0....0..0..1..0..1....0..1..0..1..0
%e A251228 ..0..0..0..1..1....0..0..0..0..1....0..0..1..0..0....1..1..0..0..0
%e A251228 ..1..0..1..1..0....1..1..0..1..0....0..0..0..0..0....1..0..0..0..1
%K A251228 nonn,tabl
%O A251228 1,1
%A A251228 _R. H. Hardin_, Nov 30 2014