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

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

R. H. Hardin, Table of n, a(n) for n = 1..180

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

Adjacent sequences: A250991 A250992 A250993 * A250995 A250996 A250997

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 29 2014

Status

approved