A303242 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 2, 4, 1, 11, 2, 8, 1, 13, 18, 3, 16, 1, 34, 8, 55, 6, 32, 1, 65, 60, 10, 181, 10, 64, 1, 123, 56, 255, 61, 494, 21, 128, 1, 266, 236, 149, 1106, 160, 1465, 42, 256, 1, 499, 428, 1676, 1373, 5158, 458, 4415, 86, 512, 1, 1037, 1248, 3307, 11111, 7823, 23995, 1748

Offset

1,3

Comments

Table starts

...1..1.....1....1......1.......1........1.........1..........1............1

...2..2....11...13.....34......65......123.......266........499.........1037

...4..2....18....8.....60......56......236.......428.......1248.........3264

...8..3....55...10....255.....149.....1676......3307......18505........65498

..16..6...181...61...1106....1373....11111.....38480.....221943......1162591

..32.10...494..160...5158....7823....90728....421983....3251872.....23282610

..64.21..1465..458..23995...41878...686376...4288552...44547581....435326091

.128.42..4415.1748.108726..277018..5320294..48315454..648070597...8762716079

.256.86.12934.6056.506416.1721671.42575026.536745912.9508520220.176408218876

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: [order 13]

k=4: [order 71] for n>72

Empirical for row n:

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

n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5

n=3: [order 20]

n=4: [order 67] for n>68

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A297870(n+2).

Sequence in context: A105619 A302212 A302460 * A302367 A303084 A302889

Adjacent sequences: A303239 A303240 A303241 * A303243 A303244 A303245

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 20 2018

Status

approved