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%I #4 Jul 04 2013 07:28:08
%S 2,3,3,4,8,4,5,16,16,5,6,30,49,30,6,7,54,132,132,54,7,8,93,341,513,
%T 341,93,8,9,153,836,1949,1949,836,153,9,10,241,1934,7131,10906,7131,
%U 1934,241,10,11,365,4232,24496,59952,59952,24496,4232,365,11,12,534,8804,78761
%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 three 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............10
%C ..3...8...16.....30......54........93........153..........241...........365
%C ..4..16...49....132.....341.......836.......1934.........4232..........8804
%C ..5..30..132....513....1949......7131......24496........78761........238146
%C ..6..54..341...1949...10906.....59952.....311644......1513042.......6877791
%C ..7..93..836...7131...59952....498772....3954995.....29333871.....203340009
%C ..8.153.1934..24496..311644...3954995...48265519....553278547....5925354448
%C ..9.241.4232..78761.1513042..29333871..553278547...9879827545..165189287060
%C .10.365.8804.238146.6877791.203340009.5925354448.165189287060.4332146485870
%H R. H. Hardin, <a href="/A227269/b227269.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 1*n + 1
%F k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 - (1/24)*n^2 + (47/12)*n - 1
%F k=3: [polynomial of degree 9] for n>3
%F k=4: [polynomial of degree 19] for n>7
%F k=5: [polynomial of degree 39] for n>15
%e Some solutions for n=4 k=4
%e ..1..1..1..1....1..1..0..0....1..1..0..0....1..1..1..1....1..1..0..0
%e ..1..0..1..1....1..1..1..0....1..1..1..1....1..1..1..0....1..0..0..0
%e ..1..1..0..1....1..1..1..0....1..1..1..1....1..1..0..0....1..0..0..0
%e ..1..1..0..1....0..1..1..0....1..0..0..0....1..1..1..0....1..0..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jul 04 2013
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