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%I #4 Oct 16 2015 07:34:17
%S 1,1,1,2,2,2,5,7,7,5,10,29,82,29,10,19,112,865,865,112,19,37,367,9888,
%T 24711,9888,367,37,73,1359,107514,826249,826249,107514,1359,73,146,
%U 5370,1260442,27274339,84790557,27274339,1260442,5370,146,293,21447,15048493
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column divisible by 7, read as a base-3 number with top and left being the most significant digits.
%C Table starts
%C ...1.....1..........2.............5.............10..............19
%C ...1.....2..........7............29............112.............367
%C ...2.....7.........82...........865...........9888..........107514
%C ...5....29........865.........24711.........826249........27274339
%C ..10...112.......9888........826249.......84790557......8491666657
%C ..19...367.....107514......27274339.....8491666657...2535097569590
%C ..37..1359....1260442.....943196037...883978450474.787253224440475
%C ..73..5370...15048493...32850517101.92359613590072
%C .146.21447..180640864.1149496602927
%C .293.86013.2167406803
%H R. H. Hardin, <a href="/A263373/b263373.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -3*a(n-4) +3*a(n-5) -2*a(n-6)
%F k=2: a(n) = 4*a(n-1) +101*a(n-6) -404*a(n-7) -2159*a(n-12) +8636*a(n-13) +2059*a(n-18) -8236*a(n-19)
%e Some solutions for n=4 k=4
%e ..1..2..2..0..1....1..1..0..1..1....2..2..0..0..1....0..2..1..2..1
%e ..2..1..2..1..0....2..2..1..2..0....1..2..2..0..1....2..2..2..1..1
%e ..2..1..0..0..0....2..1..0..2..1....0..0..0..0..0....1..2..0..1..2
%e ..2..1..0..2..1....2..1..0..0..0....0..0..0..2..1....2..1..1..1..2
%e ..2..2..1..2..0....2..0..1..1..1....0..1..2..1..1....1..1..2..2..1
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Oct 16 2015
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