A263799 - OEIS

A263799

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 nonincreasing

%I #4 Oct 26 2015 13:37:42

%S 2,2,2,3,2,3,3,3,3,3,4,3,7,3,4,4,4,7,7,4,4,5,4,14,7,14,4,5,5,5,14,17,

%T 17,14,5,5,6,5,25,18,61,18,25,5,6,6,6,25,56,130,130,56,25,6,6,7,6,41,

%U 66,494,616,494,66,41,6,7,7,7,41,218,1435,4991,4991,1435,218,41,7,7,8,7,63,272

%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 nonincreasing

%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....17......18.......56........66.......218........272.......798

%C .4.4.14..17....61.....130......494......1435......4917......13962.....41366

%C .4.4.14..18...130.....616.....4991.....30130....185795....1022105...5241463

%C .5.5.25..56...494....4991....62904....760671...8468941...90476206.850301770

%C .5.5.25..66..1435...30130...760671..20141827.445862545.9910247963

%C .6.6.41.218..4917..185795..8468941.445862545

%C .6.6.41.272.13962.1022105.90476206

%H R. H. Hardin, <a href="/A263799/b263799.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 19]

%F k=5: [order 37]

%F k=6: [order 83]

%e Some solutions for n=5 k=4

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

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

%Y Column 1 is A005578(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 26 2015