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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
15
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 27 2014
STATUS
approved