A227263 - OEIS

%I #4 Jul 04 2013 07:11:23

%S 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 1111,168,8,9,274,3136,11932,11932,3136,274,9,10,423,8065,57146,

%U 112349,57146,8065,423,10,11,625,19146,244818,937865,937865,244818,19146,625,11

%N 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 Table starts

%C ..2...3.....4.......5.........6...........7...........8...........9

%C ..3...9....23......50........96.........168.........274.........423

%C ..4..23....98.....353......1111........3136........8065.......19146

%C ..5..50...353....2201.....11932.......57146......244818......951917

%C ..6..96..1111...11932....112349......937865.....6961606....46364258

%C ..7.168..3136...57146....937865....13855163...182525275..2147322451

%C ..8.274..8065..244818...6961606...182525275..4307345460.90839025368

%C ..9.423.19146..951917..46364258..2147322451.90839025368

%C .10.625.42385.3403038.280471755.22777463128

%H R. H. Hardin, <a href="/A227263/b227263.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: a(n) = n + 1

%F k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (13/12)*n + 1

%F k=3: [polynomial of degree 9] for n>5

%F k=4: [polynomial of degree 19] for n>9

%F k=5: [polynomial of degree 39] for n>20

%e Some solutions for n=4 k=4

%e ..1..1..0..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..1..1

%e ..1..0..0..0....1..0..0..1....1..0..0..1....1..0..0..1....1..1..0..1

%e ..1..1..1..0....1..0..0..1....1..1..0..1....0..0..1..1....1..0..1..1

%e ..1..1..1..0....1..1..0..0....1..1..0..0....0..0..1..1....0..0..1..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jul 04 2013