A250583 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing max(x(i,j),x(i,j-1)) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction

10, 24, 24, 55, 60, 55, 125, 142, 142, 125, 282, 329, 336, 329, 282, 635, 758, 778, 778, 758, 635, 1428, 1743, 1779, 1776, 1779, 1743, 1428, 3210, 4009, 4077, 4013, 4013, 4077, 4009, 3210, 7214, 9223, 9346, 9055, 8914, 9055, 9346, 9223, 7214, 16211, 21227

Offset

1,1

Comments

Table starts

....10....24.....55....125....282.....635....1428....3210....7214....16211

....24....60....142....329....758....1743....4009....9223...21227....48864

....55...142....336....778...1779....4077....9346...21510...49579...114548

...125...329....778...1776...4013....9055...20510...46664..106695...244907

...282...758...1779...4013...8914...19806...44104...98902..222987...506145

...635..1743...4077...9055..19806...43202...94623..208525..463050..1035676

..1428..4009...9346..20510..44104...94623..203560..441215..963419..2122436

..3210..9223..21510..46664..98902..208525..441215..939730.2019008..4376149

..7214.21227..49579.106695.222987..463050..963419.2019008.4266332..9103961

.16211.48864.114548.244907.506145.1035676.2122436.4376149.9103961.19120668

Links

R. H. Hardin, Table of n, a(n) for n = 1..1011

Formula

Empirical for column k:

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

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

k=3: a(n) = 5*a(n-1) -6*a(n-2) -7*a(n-3) +21*a(n-4) -14*a(n-5) -a(n-6) +4*a(n-7) -a(n-8)

k=4: [order 9] for n>10

k=5: [order 12] for n>14

k=6: [order 12] for n>15

k=7: [order 15] for n>19

Example

Some solutions for n=6 k=4
..0..0..0..0..1....0..0..0..1..1....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..1....1..1..1..1..1....0..0..0..0..0....0..0..0..1..1
..1..0..0..0..1....0..1..1..1..1....0..0..0..0..0....0..0..1..0..1
..0..1..0..0..1....1..1..1..1..1....0..0..0..0..0....0..1..0..1..0
..1..0..1..1..1....1..1..1..1..1....0..0..1..1..1....1..0..1..0..1
..0..1..1..1..1....0..1..1..1..1....0..0..1..1..1....0..1..0..1..0
..1..0..1..1..1....0..1..1..1..1....0..0..1..1..1....1..0..1..0..1

Crossrefs

Sequence in context: A231880 A102089 A250797 * A223415 A187629 A175403

Adjacent sequences: A250580 A250581 A250582 * A250584 A250585 A250586

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 25 2014

Status

approved