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%I #4 Apr 09 2014 18:54:06
%S 1,2,2,4,8,4,8,25,25,8,16,81,129,81,16,32,264,637,637,264,32,64,857,
%T 3147,4989,3147,857,64,128,2785,15590,38634,38634,15590,2785,128,256,
%U 9050,77269,299329,470170,299329,77269,9050,256,512,29407,382933,2319211
%N T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly three horizontal or vertical neighbors, with new values 0..1 introduced in row major order
%C Table starts
%C ...1.....2.......4..........8...........16.............32...............64
%C ...2.....8......25.........81..........264............857.............2785
%C ...4....25.....129........637.........3147..........15590............77269
%C ...8....81.....637.......4989........38634.........299329..........2319211
%C ..16...264....3147......38634.......470170........5723270.........69637692
%C ..32...857...15590.....299329......5723270......109584463.......2097636322
%C ..64..2785...77269....2319211.....69637692.....2097636322......63213422873
%C .128..9050..382933...17971509....847232955....40145256595....1904782876182
%C .256.29407.1897681..139264013..10307784448...768275538054...57392644533582
%C .512.95557.9404215.1079178635.125409399932.14702668840259.1729241310772922
%H R. H. Hardin, <a href="/A240636/b240636.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F k=3: a(n) = 4*a(n-1) +4*a(n-2) +2*a(n-3) +7*a(n-4) +6*a(n-5) -a(n-6) -a(n-7) -a(n-8)
%F k=4: [order 32]
%e Some solutions for n=4 k=4
%e ..0..1..1..0....0..0..1..0....0..1..1..1....0..0..1..0....0..0..0..1
%e ..0..1..0..0....0..1..0..1....1..1..0..0....1..0..1..0....1..1..0..1
%e ..1..0..1..1....1..0..0..1....1..0..0..0....1..0..0..1....0..0..1..0
%e ..1..0..0..1....1..0..1..0....1..0..0..1....1..1..0..0....1..0..0..1
%Y Column 1 is A000079(n-1)
%Y Column 2 is A240478
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Apr 09 2014
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