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A263224 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column divisible by 5, read as a base-3 number with top and left being the most significant digits.

%I A263224 #4 Oct 12 2015 11:50:08
%S A263224 1,2,2,4,14,4,7,72,72,7,13,343,1009,343,13,26,1920,12601,12601,1920,
%T A263224 26,52,11444,198892,475539,198892,11444,52,103,68112,3345984,22342751,
%U A263224 22342751,3345984,68112,103,205,405019,56362801,1094138875,3126162435
%N A263224 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column divisible by 5, read as a base-3 number with top and left being the most significant digits.
%C A263224 Table starts
%C A263224 ...1......2.........4.............7...............13...................26
%C A263224 ...2.....14........72...........343.............1920................11444
%C A263224 ...4.....72......1009.........12601...........198892..............3345984
%C A263224 ...7....343.....12601........475539.........22342751...........1094138875
%C A263224 ..13...1920....198892......22342751.......3126162435.........456363243352
%C A263224 ..26..11444...3345984....1094138875.....456363243352......199878687706434
%C A263224 ..52..68112..56362801...53375395657...66317081173996....87072717791078712
%C A263224 .103.405019.951167305.2607171566653.9651690803653879.37998530090131229539
%H A263224 R. H. Hardin, <a href="/A263224/b263224.txt">Table of n, a(n) for n = 1..144</a>
%F A263224 Empirical for column k:
%F A263224 k=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)
%F A263224 k=2: [order 16]
%F A263224 k=3: [order 26]
%F A263224 k=4: [order 89]
%e A263224 Some solutions for n=3 k=4
%e A263224 ..0..0..2..0..2....0..2..1..0..2....2..2..2..0..1....2..2..2..0..1
%e A263224 ..1..1..1..2..2....1..0..2..0..1....0..0..0..0..0....0..1..0..2..2
%e A263224 ..0..0..2..2..1....2..2..1..0..0....0..0..2..0..2....2..0..2..0..0
%e A263224 ..1..1..1..1..0....0..0..2..0..2....1..1..0..0..2....0..2..0..2..0
%Y A263224 Column 1 is A262267(n-1).
%K A263224 nonn,tabl
%O A263224 1,2
%A A263224 _R. H. Hardin_, Oct 12 2015