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A266935 T(n,k)=Number of nXk binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing. 12
2, 2, 3, 2, 4, 4, 2, 4, 7, 5, 2, 5, 9, 12, 6, 2, 5, 12, 20, 19, 7, 2, 6, 14, 35, 44, 29, 8, 2, 6, 19, 52, 100, 92, 42, 9, 2, 7, 21, 82, 210, 288, 182, 59, 10, 2, 7, 26, 115, 429, 871, 794, 340, 80, 11, 2, 8, 30, 169, 816, 2577, 3566, 2077, 605, 106, 12, 2, 8, 35, 232, 1534, 7185 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
..2...2....2.....2......2.......2........2..........2.........2.........2
..3...4....4.....5......5.......6........6..........7.........7.........8
..4...7....9....12.....14......19.......21.........26........30........35
..5..12...20....35.....52......82......115........169.......232.......322
..6..19...44...100....210.....429......816.......1534......2727......4753
..7..29...92...288....871....2577.....7185......19529.....50216....125786
..8..42..182...794...3566...15850....68890.....288333...1155281...4410923
..9..59..340..2077..13899...96503...671796....4605960..30319512.191420936
.10..80..605..5110..50841..555060..6347005...73046059.821453747
.11.106.1028.11869.173470.2977370.56180274.1104862960
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)
k=3: [order 11]
k=4: [order 31]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = a(n-1) +a(n-2) -a(n-3)
n=3: a(n) = a(n-1) +a(n-2) -a(n-4) -a(n-5) +a(n-6)
n=4: [order 17]
EXAMPLE
Some solutions for n=4 k=4
..0..0..0..1....0..0..1..1....0..0..0..1....0..0..0..0....0..0..1..1
..0..1..1..0....1..1..0..0....1..1..1..0....0..0..0..0....1..1..0..0
..1..0..0..1....1..1..1..1....1..1..1..1....0..0..0..1....1..1..0..0
..1..1..1..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..1..1
CROSSREFS
Column 1 is A000027(n+1).
Column 2 is A266464.
Row 2 is A004526(n+6).
Sequence in context: A218700 A325331 A333108 * A175012 A051693 A266470
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 06 2016
STATUS
approved

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Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)