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A250994
T(n,k)=Number of (n+1)X(k+1) 0..2 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
16
40, 169, 158, 646, 872, 612, 2359, 4007, 4111, 2323, 8298, 16993, 21955, 18387, 8726, 28450, 67409, 104674, 111175, 80133, 32554, 95628, 255502, 456514, 590305, 542834, 344135, 120930, 316568, 934786, 1869400, 2800667, 3184615, 2592734, 1466191
OFFSET
1,1
COMMENTS
Table starts
......40.......169........646........2359........8298........28450
.....158.......872.......4007.......16993.......67409.......255502
.....612......4111......21955......104674......456514......1869400
....2323.....18387.....111175......590305.....2800667.....12340547
....8726.....80133.....542834.....3184615....16381510.....77449279
...32554....344135....2592734....16694358....92713991....469255626
..120930...1466191...12238954....86049801...514669302...2783159034
..447985...6219851...57388086...438901153..2820364768..16265322280
.1656600..26329263..268220043..2225675881.15340901571..94211007762
.6118822.111352239.1251995646.11253642389.83091814176.542676800586
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 6*a(n-1) -7*a(n-2) -8*a(n-3) +7*a(n-4) +6*a(n-5) +a(n-6)
k=2: [order 12]
k=3: [order 20]
k=4: [order 33]
k=5: [order 51]
k=6: [order 78]
Empirical for row n:
n=1: a(n) = 6*a(n-1) -7*a(n-2) -12*a(n-3) +15*a(n-4) +11*a(n-5) -5*a(n-6) -3*a(n-7)
n=2: [order 14]
n=3: [order 23]
n=4: [order 34]
n=5: [order 43] for n>45
n=6: [order 54] for n>58
n=7: [order 67] for n>73
EXAMPLE
Some solutions for n=3 k=4
..1..2..0..2..0....0..0..1..0..2....1..0..0..0..1....0..1..0..2..0
..1..2..0..2..0....0..1..0..1..0....1..0..0..1..0....1..0..1..0..2
..1..2..0..1..2....0..2..1..0..2....1..1..1..2..1....1..0..1..0..2
..1..2..0..1..1....1..1..2..1..0....1..1..2..1..2....1..0..1..2..0
CROSSREFS
Sequence in context: A260169 A205249 A211155 * A250995 A262487 A322774
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 29 2014
STATUS
approved