A264029 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 lexicographically nondecreasing and columns lexicographically nonincreasing.

2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 4, 3, 6, 3, 4, 4, 4, 6, 6, 4, 4, 5, 4, 10, 6, 10, 4, 5, 5, 5, 10, 10, 10, 10, 5, 5, 6, 5, 15, 10, 20, 10, 15, 5, 6, 6, 6, 15, 15, 20, 20, 15, 15, 6, 6, 7, 6, 21, 15, 35, 20, 35, 15, 21, 6, 7, 7, 7, 21, 21, 35, 35, 35, 35, 21, 21, 7, 7, 8, 7, 28, 21, 56, 35, 70, 35, 56

Offset

1,1

Comments

Table starts (empirically symmetric)

.2.2..3..3..4..4...5...5...6...6...7...7...8...8..9..9.10.10

.2.2..3..3..4..4...5...5...6...6...7...7...8...8..9..9.10

.3.3..6..6.10.10..15..15..21..21..28..28..36..36.45.45

.3.3..6..6.10.10..15..15..21..21..28..28..36..36.45

.4.4.10.10.20.20..35..35..56..56..84..84.120.120

.4.4.10.10.20.20..35..35..56..56..84..84.120

.5.5.15.15.35.35..70..70.126.126.210.210

.5.5.15.15.35.35..70..70.126.126

.6.6.21.21.56.56.126.126.252

.6.6.21.21.56.56.126.126

Links

R. H. Hardin, Table of n, a(n) for n = 1..160

Formula

Empirical for column k:

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

k=3,4: a(n) = a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5)

k=5,6: 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=7: a(n) = a(n-1) +4*a(n-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9)

Example

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

Crossrefs

Columns 1,2 (odd terms only) are A000027(n+1).

Columns 3,4 (odd terms only) are A000217(n+1).

Columns 5,6 (odd terms only) are A000292(n+1).

Column 7 (odd terms only) is A000332(n+4).

Sequence in context: A076869 A335925 A104307 * A263873 A263799 A299230

Adjacent sequences: A264026 A264027 A264028 * A264030 A264031 A264032

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 01 2015

Status

approved