A301999 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 2, 0, 2, 2, 5, 0, 3, 8, 5, 13, 0, 5, 18, 26, 15, 34, 0, 8, 50, 84, 74, 48, 89, 0, 13, 128, 309, 468, 200, 155, 233, 0, 21, 338, 1108, 2036, 2856, 530, 499, 610, 0, 34, 882, 3979, 10982, 14016, 17800, 1394, 1602, 1597, 0, 55, 2312, 14314, 53440, 122232

Offset

1,5

Comments

Table starts

.0....1....1....2.......3........5..........8..........13............21

.0....2....2....8......18.......50........128.........338...........882

.0....5....5...26......84......309.......1108........3979.........14314

.0...13...15...74.....468.....2036......10982.......53440........271596

.0...34...48..200....2856....14016.....122232......813704.......6066698

.0...89..155..530...17800...100176....1366374....12824770.....133115004

.0..233..499.1394..110036...729297...15243860...204666568....2933712940

.0..610.1602.3656..674984..5333386..169636124..3267873712...64653790404

.0.1597.5137.9578.4130664.39000114.1884309898.52110883753.1423142192108

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

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

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

k=5: [order 11] for n>12

k=6: [order 32] for n>33

k=7: [order 52] for n>54

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2)

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

n=3: [order 20]

Example

Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..0
..1..1..0..1. .1..1..0..0. .0..0..0..0. .0..1..0..0. .0..1..0..0
..1..0..1..0. .1..1..0..1. .1..1..1..1. .1..0..1..0. .1..1..0..0
..0..1..0..1. .1..0..1..0. .0..0..1..0. .0..1..0..1. .1..1..1..1
..0..0..1..1. .1..1..0..0. .0..1..0..0. .1..0..1..1. .0..0..1..1

Crossrefs

Column 2 is A001519.

Row 1 is A000045(n-1).

Row 2 is A175395(n-1).

Sequence in context: A118658 A165912 A301823 * A171936 A375372 A071055

Adjacent sequences: A301996 A301997 A301998 * A302000 A302001 A302002

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 30 2018

Status

approved