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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 4 13:53 EDT 2021. Contains 346447 sequences. (Running on oeis4.)