cp's OEIS Frontend

A250973 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements less than the absolute difference of its antidiagonal elements.

%I A250973 #6 Jul 23 2025 12:55:51
%S A250973 14,49,49,172,308,172,604,1945,1945,604,2121,12281,22048,12281,2121,
%T A250973 7448,77537,249921,249921,77537,7448,26154,489543,2833397,5089900,
%U A250973 2833397,489543,26154,91841,3090834,32124018,103684186,103684186,32124018
%N A250973 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements less than the absolute difference of its antidiagonal elements.
%C A250973 Table starts
%C A250973 ....14.......49........172..........604............2121..............7448
%C A250973 ....49......308.......1945........12281...........77537............489543
%C A250973 ...172.....1945......22048.......249921.........2833397..........32124018
%C A250973 ...604....12281.....249921......5089900.......103684186........2112130109
%C A250973 ..2121....77537....2833397....103684186......3794909318......138900769559
%C A250973 ..7448...489543...32124018...2112130109....138900769559.....9135168475316
%C A250973 .26154..3090834..364210219..43025963570...5084110136919...600808386292820
%C A250973 .91841.19514643.4129278507.876479703950.186091438754901.39514486757351514
%H A250973 R. H. Hardin, <a href="/A250973/b250973.txt">Table of n, a(n) for n = 1..420</a>
%F A250973 Empirical for column k:
%F A250973 k=1: a(n) = 4*a(n-1) -2*a(n-2) +a(n-3)
%F A250973 k=2: a(n) = 8*a(n-1) -13*a(n-2) +17*a(n-3) -14*a(n-4) +3*a(n-5)
%F A250973 k=3: [order 9]
%F A250973 k=4: [order 17]
%F A250973 k=5: [order 31]
%F A250973 k=6: [order 57] for n>58
%e A250973 Some solutions for n=3 k=4
%e A250973 ..0..0..0..0..1....0..0..0..1..1....0..1..0..0..0....0..0..0..1..0
%e A250973 ..0..0..0..1..1....0..1..1..0..0....0..1..1..1..1....1..1..1..0..1
%e A250973 ..1..1..1..0..1....1..1..0..1..1....0..1..0..0..0....1..1..0..1..0
%e A250973 ..1..1..0..1..1....0..0..1..1..0....1..1..0..0..0....0..1..0..1..1
%Y A250973 Column 1 is A010904
%K A250973 nonn,tabl
%O A250973 1,1
%A A250973 _R. H. Hardin_, Nov 29 2014