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A202335 T(n,k)=Number of (n+1)X(k+1) binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

%I A202335 #7 Jul 22 2025 16:32:49
%S A202335 16,25,25,36,48,36,49,82,82,49,64,129,162,129,64,81,191,289,289,191,
%T A202335 81,100,270,478,576,478,270,100,121,368,746,1052,1052,746,368,121,144,
%U A202335 487,1112,1796,2102,1796,1112,487,144,169,629,1597,2906,3896,3896,2906,1597
%N A202335 T(n,k)=Number of (n+1)X(k+1) binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
%C A202335 Table starts
%C A202335 ..16..25...36...49....64....81....100....121....144.....169.....196.....225
%C A202335 ..25..48...82..129...191...270....368....487....629.....796.....990....1213
%C A202335 ..36..82..162..289...478...746...1112...1597...2224....3018....4006....5217
%C A202335 ..49.129..289..576..1052..1796...2906...4501...6723....9739...13743...18958
%C A202335 ..64.191..478.1052..2102..3896...6800..11299..18020...27757...41498...60454
%C A202335 ..81.270..746.1796..3896..7790..14588..25885..43903...71658..113154..173606
%C A202335 .100.368.1112.2906..6800.14588..29174..55057..98958..170614..283766..457370
%C A202335 .121.487.1597.4501.11299.25885..55057.110112.209068..379680..663444.1120812
%C A202335 .144.629.2224.6723.18020.43903..98958.209068.418134..797812.1461254.2582064
%C A202335 .169.796.3018.9739.27757.71658.170614.379680.797812.1595622.3056874.5638936
%H A202335 R. H. Hardin, <a href="/A202335/b202335.txt">Table of n, a(n) for n = 1..10018</a>
%e A202335 Some solutions for n=5 k=3
%e A202335 ..0..0..1..0....0..0..1..0....0..0..1..0....0..0..1..0....0..0..1..1
%e A202335 ..0..0..1..0....0..0..1..0....0..1..1..1....0..0..1..0....0..0..1..1
%e A202335 ..0..0..1..0....0..0..1..0....0..1..1..1....0..0..1..0....0..0..1..1
%e A202335 ..0..0..1..1....0..0..1..0....0..1..1..1....0..0..1..0....0..1..1..1
%e A202335 ..0..0..1..1....0..0..1..0....0..1..1..1....0..0..1..0....0..1..1..1
%e A202335 ..0..1..1..1....0..0..1..1....0..1..1..1....0..1..1..1....0..1..1..1
%Y A202335 Column 1 is A000290(n+3)
%Y A202335 Column 2 is A110610(n+3)
%K A202335 nonn,tabl
%O A202335 1,1
%A A202335 _R. H. Hardin_ Dec 17 2011