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%I #4 Jan 12 2014 06:05:22
%S 16,46,46,120,202,120,288,814,814,288,660,2878,5567,2878,660,1456,
%T 9320,33851,33851,9320,1456,3136,27731,184281,378570,184281,27731,
%U 3136,6624,77606,892122,3824372,3824372,892122,77606,6624,13808,205571,3925717
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the sum of each 2X2 subblock two extreme terms minus its two median terms lexicographically nondecreasing rowwise and columnwise
%C Table starts
%C ....16......46.......120.........288...........660...........1456
%C ....46.....202.......814........2878..........9320..........27731
%C ...120.....814......5567.......33851........184281.........892122
%C ...288....2878.....33851......378570.......3824372.......33823017
%C ...660....9320....184281.....3824372......74362722.....1271453587
%C ..1456...27731....892122....33823017....1271453587....42883865335
%C ..3136...77606...3925717...265989722...19182239308..1280647786349
%C ..6624..205571..15834473..1875119528..256273383832.33729294480195
%C .13808..522118..59506551.12064334056.3086943812776
%C .28480.1277701.209811804.71470709789
%H R. H. Hardin, <a href="/A235555/b235555.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +4*a(n-2) -8*a(n-3) -4*a(n-4) +8*a(n-5)
%F k=2: [order 19]
%F k=3: [order 55]
%e Some solutions for n=3 k=4
%e ..1..1..1..0..0....0..1..0..1..0....1..1..0..0..0....1..1..0..1..0
%e ..1..0..0..1..0....1..1..1..1..1....0..1..1..1..1....0..1..1..1..1
%e ..1..1..0..0..0....0..1..1..1..1....1..0..0..1..1....1..0..0..0..0
%e ..0..0..1..0..1....0..0..1..0..1....0..0..1..0..0....0..1..0..1..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 12 2014
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