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A251249 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the sum of its diagonal elements less than the minimum of its antidiagonal elements.

%I A251249 #6 Jul 23 2025 13:12:42
%S A251249 75,621,621,5139,14265,5139,42525,327753,327753,42525,351891,7530633,
%T A251249 20904689,7530633,351891,2911869,173028393,1333268433,1333268433,
%U A251249 173028393,2911869,24095475,3975606801,85032883789,236035946835
%N A251249 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the sum of its diagonal elements less than the minimum of its antidiagonal elements.
%C A251249 Table starts
%C A251249 ......75........621..........5139............42525...............351891
%C A251249 .....621......14265........327753..........7530633............173028393
%C A251249 ....5139.....327753......20904689.......1333268433..........85032883789
%C A251249 ...42525....7530633....1333268433.....236035946835.......41786532918513
%C A251249 ..351891..173028393...85032883789...41786532918513....20534495636679387
%C A251249 .2911869.3975606801.5423196612609.7397658897202791.10090935221593972941
%H A251249 R. H. Hardin, <a href="/A251249/b251249.txt">Table of n, a(n) for n = 1..264</a>
%F A251249 Empirical for column k:
%F A251249 k=1: a(n) = 9*a(n-1) -6*a(n-2)
%F A251249 k=2: a(n) = 27*a(n-1) -94*a(n-2) +36*a(n-3) -4*a(n-4) -36*a(n-5)
%F A251249 k=3: [order 10]
%F A251249 k=4: [order 24]
%F A251249 k=5: [order 51]
%e A251249 Some solutions for n=2 k=4
%e A251249 ..0..0..0..0..0....0..0..0..2..2....0..0..0..2..0....0..0..0..2..0
%e A251249 ..0..2..1..1..0....0..0..1..1..2....0..0..0..0..1....0..1..1..1..0
%e A251249 ..0..2..1..2..2....0..0..2..1..1....0..2..0..1..2....0..0..0..1..0
%Y A251249 Column 1 is A190983(n+2)
%K A251249 nonn,tabl
%O A251249 1,1
%A A251249 _R. H. Hardin_, Dec 01 2014