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A184548 T(n,k)=Number of (n+2)X(k+2) binary arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

%I A184548 #10 Jul 22 2025 09:37:18
%S A184548 45,89,89,147,193,147,220,340,340,220,309,537,631,537,309,415,792,
%T A184548 1048,1048,792,415,539,1114,1627,1837,1627,1114,539,682,1513,2413,
%U A184548 3024,3024,2413,1513,682,845,2000,3461,4774,5313,4774,3461,2000,845,1029,2587,4837
%N A184548 T(n,k)=Number of (n+2)X(k+2) binary arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
%C A184548 Table starts
%C A184548 ...45...89..147...220...309....415....539....682.....845....1029....1235
%C A184548 ...89..193..340...537...792...1114...1513...2000....2587....3287....4114
%C A184548 ..147..340..631..1048..1627...2413...3461...4837....6619....8898...11779
%C A184548 ..220..537.1048..1837..3024...4774...7307..10909...15944...22867...32238
%C A184548 ..309..792.1627..3024..5313...8989..14767..23648...36997...56634...84939
%C A184548 ..415.1114.2413..4774..8989..16345..28844..49489...82648..134509..213640
%C A184548 ..539.1513.3461..7307.14767..28844..54543..99872..177207..305112..510719
%C A184548 ..682.2000.4837.10909.23648..49489..99872.194245..364432..660821.1160932
%C A184548 ..845.2587.6619.15944.36997..82648.177207.364432..719905.1369596.2516995
%C A184548 .1029.3287.8898.22867.56634.134509.305112.660821.1369596.2725367.5225554
%H A184548 R. H. Hardin, <a href="/A184548/b184548.txt">Table of n, a(n) for n = 1..9378</a>
%H A184548 R. H. Hardin, <a href="/A184548/a184548.txt">Polynomials for columns 1-8</a>
%F A184548 Empirical: T(n,k) is a polynomial of degree k+2 in n, for fixed k.
%F A184548 Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.
%F A184548 Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.
%e A184548 Some solutions for 5X4
%e A184548 ..0..0..0..1....0..0..0..1....0..0..0..0....0..0..0..1....0..0..0..0
%e A184548 ..0..0..1..1....0..0..0..1....0..0..0..0....0..0..1..1....0..0..0..0
%e A184548 ..0..0..1..1....0..0..1..1....0..0..0..0....0..0..1..1....0..0..0..0
%e A184548 ..0..1..0..0....0..1..0..1....0..0..0..1....0..1..1..1....0..0..1..1
%e A184548 ..1..1..0..0....1..1..0..1....1..1..1..0....0..1..1..1....1..1..0..1
%K A184548 nonn,tabl
%O A184548 1,1
%A A184548 _R. H. Hardin_, general degree formula intuited by _D. S. McNeil_ in the Sequence Fans Mailing List, Jan 16 2011