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%I #4 Oct 04 2015 10:13:40
%S 1,1,2,1,3,3,1,6,5,5,1,11,15,9,10,1,22,33,53,27,19,1,43,99,137,318,61,
%T 37,1,86,261,853,1411,1207,145,74,1,171,783,2953,18190,7417,5797,435,
%U 147,1,342,2241,17333,121507,152587,51769,34782,1253,293,1,683,6723,71721
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.
%C Table starts
%C ...1....1.......1........1...........1...........1............1...........1
%C ...2....3.......6.......11..........22..........43...........86.........171
%C ...3....5......15.......33..........99.........261..........783........2241
%C ...5....9......53......137.........853........2953........17333.......71721
%C ..10...27.....318.....1411.......18190......121507......1444558....12031011
%C ..19...61....1207.....7417......152587.....1550557.....30497815...420921961
%C ..37..145....5797....51769.....2045269....33948145...1282949605.32134185721
%C ..74..435...34782...529931....42299374..1361585275.102437680622
%C .147.1253..189135..4701201...727767387.42115306149
%C .293.3593.1089701.44632313.13958567845
%H R. H. Hardin, <a href="/A262917/b262917.txt">Table of n, a(n) for n = 1..112</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 15]
%F Empirical for row n:
%F n=2: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)
%F n=3: a(n) = 3*a(n-1) +3*a(n-2) -9*a(n-3)
%F n=4: [order 8]
%F n=5: [order 10]
%F n=6: [order 65]
%e Some solutions for n=4 k=4
%e ..0..0..1..1..0....0..1..1..1..1....1..0..0..1..0....0..0..0..0..0
%e ..1..1..0..0..0....0..1..1..0..0....1..1..0..0..0....0..0..0..0..0
%e ..1..1..1..1..0....0..1..1..1..1....1..1..0..1..1....0..0..1..1..0
%e ..1..1..0..0..0....0..0..0..0..0....0..1..0..0..1....0..0..1..1..0
%e ..0..0..1..1..0....0..0..0..1..1....0..0..0..1..1....0..0..1..1..0
%Y Column 1 is A046630(n-1).
%Y Column 2 is A262314(n-1).
%Y Row 2 is A005578(n+1).
%Y Row 3 is A262326.
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Oct 04 2015
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