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T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each row and column divisible by 7, read as a binary number with top and left being the most significant bits.
6

%I #4 Sep 17 2015 22:23:41

%S 2,3,3,5,5,5,10,9,9,10,19,27,17,27,19,37,61,133,133,61,37,74,145,361,

%T 1618,361,145,74,147,435,1009,6043,6043,1009,435,147,293,1253,8357,

%U 42661,37873,42661,8357,1253,293,586,3593,33993,683218,413893,413893,683218

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each row and column divisible by 7, read as a binary number with top and left being the most significant bits.

%C Table starts

%C ...2.....3......5.......10........19........37........74........147........293

%C ...3.....5......9.......27........61.......145.......435.......1253.......3593

%C ...5.....9.....17......133.......361......1009......8357......33993.....127121

%C ..10....27....133.....1618......6043.....42661....683218....4276587...39384421

%C ..19....61....361.....6043.....37873....413893...8003035..103003837.1659181705

%C ..37...145...1009....42661....413893...7914829.281951533.7901300449

%C ..74...435...8357...683218...8003035.281951533

%C .147..1253..33993..4276587.103003837

%C .293..3593.127121.39384421

%C .586.10779.795013

%H R. H. Hardin, <a href="/A262319/b262319.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

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

%F k=2: [order 15]

%F k=3: [order 43]

%F k=4: [order 29]

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%Y Column 1 is A046630.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Sep 17 2015