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.

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

Offset: 1

Author

R. H. Hardin, Oct 26 2015

Keywords

• nonn
• tabl

Comments

Table starts

.2.2..3...3.....4.......4........5.........5.........6..........6.........7

.2.2..3...3.....4.......4........5.........5.........6..........6.........7

.3.3..7...7....14......14.......25........25........41.........41........63

.3.3..7...7....17......18.......56........66.......218........272.......798

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

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

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

.5.5.25..66..1435...30130...760671..20141827.445862545.9910247963

.6.6.41.218..4917..185795..8468941.445862545

.6.6.41.272.13962.1022105.90476206

Examples

			Some solutions for n=5 k=4
..1..1..0..0..0....1..1..1..1..0....1..1..0..0..0....1..1..0..0..0
..1..1..0..0..0....1..1..1..1..0....1..1..0..0..0....1..1..0..0..0
..1..1..0..0..0....1..1..1..1..0....1..1..0..0..0....1..1..0..0..0
..1..1..0..0..0....1..1..1..1..0....1..1..0..0..0....1..1..0..0..0
..0..0..1..1..0....1..1..1..1..0....0..0..0..0..0....1..1..0..0..0
..0..0..1..1..0....1..1..1..1..0....0..0..0..0..0....1..1..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..144

Crossrefs

Column 1 is A005578(n+1).

Formula

Empirical for column k:

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

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

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)

k=4: [order 19]

k=5: [order 37]

k=6: [order 83]