A263439 - OEIS

%I #4 Oct 18 2015 10:56:51

%S 1,2,2,4,21,4,6,180,180,6,9,1225,6945,1225,9,18,9820,230997,230997,

%T 9820,18,36,90785,9407092,34701974,9407092,90785,36,61,841164,

%U 408471412,7338416019,7338416019,408471412,841164,61,106,7551453,18332843169

%N T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with each row and column divisible by 13, read as a base-5 number with top and left being the most significant digits.

%C Table starts

%C ...1........2............4...............6................9...............18

%C ...2.......21..........180............1225.............9820............90785

%C ...4......180.........6945..........230997..........9407092........408471412

%C ...6.....1225.......230997........34701974.......7338416019....1734077050001

%C ...9.....9820......9407092......7338416019....8252778348422.9899034266254567

%C ..18....90785....408471412...1734077050001.9899034266254567

%C ..36...841164..18332843169.411888488700205

%C ..61..7551453.844323031241

%C .106.69952442

%C .212

%H R. H. Hardin, <a href="/A263439/b263439.txt">Table of n, a(n) for n = 1..60</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +9*a(n-4) -18*a(n-5) -14*a(n-8) +28*a(n-9) +a(n-12) -2*a(n-13)

%F k=2: [order 88]

%e Some solutions for n=3 k=4

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

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

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

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Oct 18 2015