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A227263 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

%I A227263 #6 Jul 23 2025 05:35:46
%S A227263 2,3,3,4,9,4,5,23,23,5,6,50,98,50,6,7,96,353,353,96,7,8,168,1111,2201,
%T A227263 1111,168,8,9,274,3136,11932,11932,3136,274,9,10,423,8065,57146,
%U A227263 112349,57146,8065,423,10,11,625,19146,244818,937865,937865,244818,19146,625,11
%N A227263 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.
%C A227263 Table starts
%C A227263 ..2...3.....4.......5.........6...........7...........8...........9
%C A227263 ..3...9....23......50........96.........168.........274.........423
%C A227263 ..4..23....98.....353......1111........3136........8065.......19146
%C A227263 ..5..50...353....2201.....11932.......57146......244818......951917
%C A227263 ..6..96..1111...11932....112349......937865.....6961606....46364258
%C A227263 ..7.168..3136...57146....937865....13855163...182525275..2147322451
%C A227263 ..8.274..8065..244818...6961606...182525275..4307345460.90839025368
%C A227263 ..9.423.19146..951917..46364258..2147322451.90839025368
%C A227263 .10.625.42385.3403038.280471755.22777463128
%H A227263 R. H. Hardin, <a href="/A227263/b227263.txt">Table of n, a(n) for n = 1..112</a>
%F A227263 Empirical for column k:
%F A227263 k=1: a(n) = n + 1
%F A227263 k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (13/12)*n + 1
%F A227263 k=3: [polynomial of degree 9] for n>5
%F A227263 k=4: [polynomial of degree 19] for n>9
%F A227263 k=5: [polynomial of degree 39] for n>20
%e A227263 Some solutions for n=4 k=4
%e A227263 ..1..1..0..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..1..1
%e A227263 ..1..0..0..0....1..0..0..1....1..0..0..1....1..0..0..1....1..1..0..1
%e A227263 ..1..1..1..0....1..0..0..1....1..1..0..1....0..0..1..1....1..0..1..1
%e A227263 ..1..1..1..0....1..1..0..0....1..1..0..0....0..0..1..1....0..0..1..1
%K A227263 nonn,tabl
%O A227263 1,1
%A A227263 _R. H. Hardin_ Jul 04 2013