A251317 - OEIS

%I #4 Dec 01 2014 13:50:55

%S 10,25,25,61,79,61,149,238,238,149,365,720,890,720,365,894,2199,3369,

%T 3369,2199,894,2189,6717,12859,16006,12859,6717,2189,5360,20484,48980,

%U 76167,76167,48980,20484,5360,13125,62464,186162,361845,451826,361845

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements

%C Table starts

%C ....10.....25.......61.......149........365.........894..........2189

%C ....25.....79......238.......720.......2199........6717.........20484

%C ....61....238......890......3369......12859.......48980........186162

%C ...149....720.....3369.....16006......76167......361845.......1720147

%C ...365...2199....12859.....76167.....451826.....2688099......16024915

%C ...894...6717....48980....361845....2688099....20080487.....149982413

%C ..2189..20484...186162...1720147...16024915...149982413....1401489913

%C ..5360..62464...707897...8186775...95495471..1118147932...13088358653

%C .13125.190542..2693783..38968823..568712168..8339278058..122472226217

%C .32139.581259.10250631.185439356.3387770571.62282522930.1147464543755

%H R. H. Hardin, <a href="/A251317/b251317.txt">Table of n, a(n) for n = 1..759</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -a(n-4)

%F k=2: a(n) = 5*a(n-1) -9*a(n-2) +13*a(n-3) -13*a(n-4) +6*a(n-5) -2*a(n-6)

%F k=3: [order 10]

%F k=4: [order 15] for n>17

%F k=5: [order 26] for n>27

%F k=6: [order 42] for n>44

%F k=7: [order 68] for n>70

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 01 2014