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A254457 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock diagonal maximum minus antidiagonal median nondecreasing horizontally and vertically.

%I A254457 #6 Jul 23 2025 14:41:58
%S A254457 512,3036,3036,16240,26380,16240,76832,196684,196684,76832,348032,
%T A254457 1279568,2085712,1279568,348032,1511152,8004340,19716320,19716320,
%U A254457 8004340,1511152,6440848,48345120,180449544,275772848,180449544,48345120
%N A254457 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock diagonal maximum minus antidiagonal median nondecreasing horizontally and vertically.
%C A254457 Table starts
%C A254457 .....512......3036.......16240........76832.........348032..........1511152
%C A254457 ....3036.....26380......196684......1279568........8004340.........48345120
%C A254457 ...16240....196684.....2085712.....19716320......180449544.......1621936236
%C A254457 ...76832...1279568....19716320....275772848.....3694478768......48236381800
%C A254457 ..348032...8004340...180449544...3694478768....71814202464....1361600709160
%C A254457 .1511152..48345120..1621936236..48236381800..1361600709160...37859718002056
%C A254457 .6440848.289945200.14531913928.623402653056.25559706957728.1041397026476012
%H A254457 R. H. Hardin, <a href="/A254457/b254457.txt">Table of n, a(n) for n = 1..219</a>
%F A254457 Empirical for column k:
%F A254457 k=1: [linear recurrence of order 32]
%F A254457 k=2: [order 47] for n>61
%F A254457 k=3: [order 73] for n>90
%e A254457 Some solutions for n=2 k=4
%e A254457 ..0..0..1..0..0..0....0..0..1..0..0..0....0..0..0..1..1..0....0..0..0..1..1..0
%e A254457 ..1..0..0..1..0..0....0..0..1..1..0..0....0..0..1..0..0..0....1..0..0..0..1..0
%e A254457 ..1..1..1..0..0..0....1..1..1..1..1..0....1..1..0..0..0..0....1..0..0..0..0..1
%e A254457 ..1..0..0..0..1..0....0..1..1..0..0..0....0..0..0..1..1..1....0..0..0..1..1..1
%Y A254457 Column 1 is A254161
%K A254457 nonn,tabl
%O A254457 1,1
%A A254457 _R. H. Hardin_, Jan 30 2015