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T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with each row and column divisible by 9, read as a base-5 number with top and left being the most significant digits.
9

%I #4 Oct 16 2015 08:14:50

%S 2,4,4,11,38,11,31,496,496,31,89,6731,34334,6731,89,253,93378,2332320,

%T 2332320,93378,253,748,1302087,161833750,787486033,161833750,1302087,

%U 748,2214,18221996,11300297029,271477636708,271477636708,11300297029

%N T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with each row and column divisible by 9, read as a base-5 number with top and left being the most significant digits.

%C Table starts

%C ....2.........4.............11...................31........................89

%C ....4........38............496.................6731.....................93378

%C ...11.......496..........34334..............2332320.................161833750

%C ...31......6731........2332320............787486033..............271477636708

%C ...89.....93378......161833750.........271477636708...........466607833464165

%C ..253...1302087....11300297029.......94234480080401........808208250265441905

%C ..748..18221996...790807552035....32785038500076147....1403458538939419648545

%C .2214.255080336.55354924698596.11408914805662871537.2437738823003642650564362

%H R. H. Hardin, <a href="/A263382/b263382.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) -9*a(n-3) +3*a(n-6) -9*a(n-7) -9*a(n-8) +27*a(n-9)

%F k=2: [order 51]

%e Some solutions for n=3 k=4

%e ..0..3..0..0..3....1..3..1..2..0....0..1..3..3..1....0..3..4..0..2

%e ..1..4..0..1..4....0..3..3..0..0....1..4..0..1..4....0..0..1..2..1

%e ..0..0..0..0..0....0..0..1..2..1....0..1..2..1..0....0..0..3..4..4

%e ..2..2..0..2..2....1..0..2..1..4....2..4..2..0..0....0..3..0..2..2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 16 2015