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A250956 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having its maximum diagonal element less than its minimum antidiagonal element.

%I A250956 #6 Jul 23 2025 12:54:06
%S A250956 15,56,56,209,392,209,780,2744,2744,780,2911,19208,36016,19208,2911,
%T A250956 10864,134456,472712,472712,134456,10864,40545,941192,6204344,
%U A250956 11633448,6204344,941192,40545,151316,6588344,81431944,286298344,286298344
%N A250956 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having its maximum diagonal element less than its minimum antidiagonal element.
%C A250956 Table starts
%C A250956 .....15.......56.........209...........780.............2911..............10864
%C A250956 .....56......392........2744.........19208...........134456.............941192
%C A250956 ....209.....2744.......36016........472712..........6204344...........81431944
%C A250956 ....780....19208......472712......11633448........286298344.........7045780240
%C A250956 ...2911...134456.....6204344.....286298344......13211127617.......609622239024
%C A250956 ..10864...941192....81431944....7045780240.....609622239024.....52746349035592
%C A250956 ..40545..6588344..1068793208..173396103624...28130774228952...4563772381621072
%C A250956 .151316.46118408.14027896712.4267264603784.1298083303266168.394871276236514256
%H A250956 R. H. Hardin, <a href="/A250956/b250956.txt">Table of n, a(n) for n = 1..759</a>
%F A250956 Empirical for column k:
%F A250956 k=1: a(n) = 4*a(n-1) -a(n-2)
%F A250956 k=2: a(n) = 7*a(n-1)
%F A250956 k=3: a(n) = 15*a(n-1) -24*a(n-2) -8*a(n-3)
%F A250956 k=4: a(n) = 27*a(n-1) -57*a(n-2) -46*a(n-3) +30*a(n-4)
%F A250956 k=5: [order 7]
%F A250956 k=6: [order 9]
%F A250956 k=7: [order 16]
%e A250956 Some solutions for n=3 k=4
%e A250956 ..0..0..1..0..1....0..1..0..0..0....0..0..0..1..1....0..1..0..1..1
%e A250956 ..0..0..0..1..1....0..1..1..1..0....0..1..0..0..0....0..1..0..0..0
%e A250956 ..0..1..1..1..0....0..0..0..1..1....0..0..1..0..0....0..0..0..0..0
%e A250956 ..0..0..1..1..0....1..1..0..0..1....1..0..1..0..1....0..1..0..0..1
%Y A250956 Column 1 is A001353(n+2)
%Y A250956 Column 2 is A003950(n+1)
%K A250956 nonn,tabl
%O A250956 1,1
%A A250956 _R. H. Hardin_, Nov 28 2014