A263873 - OEIS

A263873

T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nondecreasing.

%I #4 Oct 28 2015 11:50:30

%S 2,2,2,3,2,3,3,3,3,3,4,3,7,3,4,4,4,7,7,4,4,5,4,14,7,14,4,5,5,5,14,16,

%T 16,14,5,5,6,5,25,17,61,17,25,5,6,6,6,25,41,93,93,41,25,6,6,7,6,41,48,

%U 494,379,494,48,41,6,7,7,7,41,113,975,2909,2909,975,113,41,7,7,8,7,63,141

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nondecreasing.

%C Table starts

%C .2.2..3...3.....4......4........5.........5.........6..........6.........7

%C .3.3..7...7....14.....14.......25........25........41.........41........63

%C .3.3..7...7....16.....17.......41........48.......113........141.......303

%C .4.4.14..16....61.....93......494.......975......4917......10340.....41366

%C .4.4.14..17....93....379.....2909.....20374....121878.....785046...3811314

%C .5.5.25..41...494...2909....62904....525967...8468941...71260394.850301770

%C .5.5.25..48...975..20374...525967..16701495.329866231.8672875293

%C .6.6.41.113..4917.121878..8468941.329866231

%C .6.6.41.141.10340.785046.71260394

%H R. H. Hardin, <a href="/A263873/b263873.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2) -a(n-3)

%F k=2: a(n) = a(n-1) +a(n-2) -a(n-3)

%F k=3: a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7)

%F k=4: [order 14]

%F k=5: [order 37]

%F k=6: [order 79]

%e Some solutions for n=4 k=4

%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0

%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..1..1..1..1

%e ..0..0..0..1..1....0..1..1..1..1....0..0..0..0..0....0..1..1..1..1

%Y Columns 1 and 2 are A004526(n+3).

%Y Column 3 is A263794(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 28 2015