|
%I #6 Dec 28 2014 08:10:43
%S 16,39,39,69,72,69,109,88,88,109,181,120,94,120,181,325,192,129,129,
%T 192,325,613,336,201,164,201,336,613,1189,624,345,236,236,345,624,
%U 1189,2341,1200,633,380,308,380,633,1200,2341,4645,2352,1209,668,452,452,668,1209
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically
%C Table starts
%C ...16...39...69..109..181..325..613.1189.2341.4645..9253.18469.36901.73765
%C ...39...72...88..120..192..336..624.1200.2352.4656..9264.18480.36912.73776
%C ...69...88...94..129..201..345..633.1209.2361.4665..9273.18489.36921.73785
%C ..109..120..129..164..236..380..668.1244.2396.4700..9308.18524.36956.73820
%C ..181..192..201..236..308..452..740.1316.2468.4772..9380.18596.37028.73892
%C ..325..336..345..380..452..596..884.1460.2612.4916..9524.18740.37172.74036
%C ..613..624..633..668..740..884.1172.1748.2900.5204..9812.19028.37460.74324
%C .1189.1200.1209.1244.1316.1460.1748.2324.3476.5780.10388.19604.38036.74900
%C .2341.2352.2361.2396.2468.2612.2900.3476.4628.6932.11540.20756.39188.76052
%C .4645.4656.4665.4700.4772.4916.5204.5780.6932.9236.13844.23060.41492.78356
%H R. H. Hardin, <a href="/A253159/b253159.txt">Table of n, a(n) for n = 1..1243</a>
%F Empirical for rows, columns, diagonal: a(n) = 3*a(n-1) -2*a(n-2) for n>5
%F Empirical for max(n,k)>3: T(n,k) = 9*2^(n-1) + 9*2^(k-1) + c, where c=28 for min(n,k)=1, c=30 for min(n,k)=2, c=21 for min(n,k)=3, c=20 for min(n,k)>3
%F (no formula for the upper left 3X3 portion)
%e Some solutions for n=6 k=4
%e ..1..1..1..1..1....0..0..0..0..0....0..1..1..1..1....0..0..0..0..0
%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e ..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
%e ..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
%e ..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....1..1..1..1..1
%e ..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
%e ..1..1..1..1..1....0..0..0..0..1....1..1..1..1..1....1..1..1..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 28 2014
| 