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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A052542(n+2)

Sequence in context: A187621 A231880 A102089 * A250583 A223415 A187629

Adjacent sequences: A250794 A250795 A250796 * A250798 A250799 A250800

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 27 2014

Status

approved