A251100 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having its minimum diagonal element less than its minimum antidiagonal element

13, 41, 41, 129, 212, 129, 406, 1109, 1109, 406, 1278, 5817, 9597, 5817, 1278, 4023, 30517, 82814, 82814, 30517, 4023, 12664, 160086, 713769, 1175519, 713769, 160086, 12664, 39865, 839758, 6151051, 16697127, 16697127, 6151051, 839758, 39865

Offset

1,1

Comments

Table starts

.....13........41.........129...........406.............1278...............4023

.....41.......212........1109..........5817............30517.............160086

....129......1109........9597.........82814...........713769............6151051

....406......5817.......82814.......1175519.........16697127..........237288487

...1278.....30517......713769......16697127........391088995.........9160138107

...4023....160086.....6151051.....237288487.......9160138107.......353489877714

..12664....839758....53009570....3372537762.....214512524583.....13640572890821

..39865...4405079...456842112...47933018061....5023196973684....526395665662695

.125491..23107524..3937123328..681254534234..117627015646158..20314343818684906

.395033.121214121.33930621210.9682407527191.2754453306431041.783961045672945429

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Formula

Empirical for column k:

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

k=2: a(n) = 7*a(n-1) -11*a(n-2) +10*a(n-3) -3*a(n-4)

k=3: [order 9]

k=4: [order 17]

k=5: [order 31]

k=6: [order 57] for n>58

Example

Some solutions for n=3 k=4
..0..0..1..1..0....0..1..1..0..1....1..1..1..0..0....0..0..1..1..0
..0..0..0..1..1....0..1..1..0..1....0..0..1..0..0....1..0..0..0..0
..0..0..0..0..1....0..0..1..0..0....0..0..0..0..0....0..0..0..1..0
..0..1..1..0..1....1..0..1..1..1....1..0..0..1..0....0..0..0..1..0

Crossrefs

Column 1 is A052529(n+2)

Sequence in context: A319088 A041755 A229768 * A044968 A108226 A337146

Adjacent sequences: A251097 A251098 A251099 * A251101 A251102 A251103

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 29 2014

Status

approved