A250797 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

10, 24, 24, 54, 66, 58, 118, 162, 180, 140, 252, 376, 482, 490, 338, 530, 838, 1190, 1430, 1336, 816, 1102, 1818, 2776, 3776, 4258, 3646, 1970, 2272, 3868, 6230, 9258, 12062, 12706, 9956, 4756, 4654, 8114, 13598, 21610, 31220, 38676, 37986, 27194, 11482

Offset: 1

Author

R. H. Hardin, Nov 27 2014

Keywords

• nonn
• tabl

Comments

Table starts

....10.....24......54.....118......252......530......1102......2272......4654

....24.....66.....162.....376......838.....1818......3868......8114.....16842

....58....180.....482....1190.....2776.....6230.....13598.....29084.....61274

...140....490....1430....3776.....9258....21610.....48600....106426....228342

...338...1336....4258...12062....31220....76110....177142....398704....874298

...816...3646...12706...38676...105954...270598....653880...1517666...3411886

..1970...9956...37986..124366...361344...968942...2437366...5849556..13519146

..4756..27194..113694..400616..1236058..3485538...9144752..22741458..54152230

.11482..74288..340562.1292134..4237556.12580830..34478398..88996688.218754226

.27720.202950.1020650.4171276.14549610.45517150.130446176.349951066.889238238

Examples

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

Links

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

Crossrefs

Column 1 is A052542(n+2)

Formula

Empirical for column k:

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

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

k=3: a(n) = 6*a(n-1) -10*a(n-2) +11*a(n-4) -6*a(n-5)

k=4: a(n) = 8*a(n-1) -20*a(n-2) +8*a(n-3) +33*a(n-4) -36*a(n-5) +8*a(n-7)

k=5: [order 9]

k=6: [order 11]

k=7: [order 13]

Empirical for row n:

n=1: a(n) = 3*a(n-1) -a(n-2) -2*a(n-3)

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

n=3: a(n) = 5*a(n-1) -8*a(n-2) +3*a(n-3) +3*a(n-4) -2*a(n-5)

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

n=5: [order 9]

n=6: [order 12]

n=7: [order 13]