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.

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

Offset

1,1

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....16.....17.......41........48.......113........141.......303

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

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

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

.5.5.25..48...975..20374...525967..16701495.329866231.8672875293

.6.6.41.113..4917.121878..8468941.329866231

.6.6.41.141.10340.785046.71260394

Links

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

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 14]

k=5: [order 37]

k=6: [order 79]

Example

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

Crossrefs

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

Column 3 is A263794(n+1).

Sequence in context: A335925 A104307 A264029 * A263799 A299230 A182576

Adjacent sequences: A263870 A263871 A263872 * A263874 A263875 A263876

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 28 2015

Status

approved