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%I #4 Jan 10 2014 06:54:24
%S 16,44,44,121,172,121,286,704,704,286,676,2302,4256,2302,676,1482,
%T 7617,20398,20398,7617,1482,3249,21707,98575,150862,98575,21707,3249,
%U 6840,62070,397340,1155953,1155953,397340,62070,6840,14400,160219,1623115
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with 2X2 subblock sums lexicographically nondecreasing rowwise and nonincreasing columnwise
%C Table starts
%C ....16.....44......121........286...........676............1482
%C ....44....172......704.......2302..........7617...........21707
%C ...121....704.....4256......20398.........98575..........397340
%C ...286...2302....20398.....150862.......1155953.........7379380
%C ...676...7617....98575....1155953......13930916.......145005714
%C ..1482..21707...397340....7379380.....145005714......2573684600
%C ..3249..62070..1623115...48788187....1561049902.....48150637857
%C ..6840.160219..5744912..273307984...14369333157....775525688659
%C .14400.413728.20612708.1578043496..137304769214..13190905086499
%C .29640.994013.65877470.7881635316.1126706100728.190687328015653
%H R. H. Hardin, <a href="/A235413/b235413.txt">Table of n, a(n) for n = 1..143</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -18*a(n-3) +17*a(n-4) +22*a(n-5) -36*a(n-6) +20*a(n-8) -8*a(n-9)
%F k=2: [order 31]
%F k=3: [order 73]
%e Some solutions for n=4 k=4
%e ..0..0..0..0..0....0..0..0..0..0....1..0..0..0..0....1..0..0..0..0
%e ..1..0..1..0..1....1..1..0..0..0....1..1..1..0..1....1..0..1..0..0
%e ..0..0..0..0..0....0..0..0..0..0....1..0..0..1..0....1..1..0..0..1
%e ..1..1..1..1..1....1..1..0..0..0....1..1..1..0..1....1..1..1..0..1
%e ..1..0..1..0..0....0..1..1..0..1....1..1..1..0..0....1..1..1..0..0
%Y Column 1 is A204032
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 10 2014
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