A302212 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 2, 4, 1, 11, 2, 8, 1, 13, 16, 3, 16, 1, 34, 5, 47, 6, 32, 1, 65, 32, 7, 147, 10, 64, 1, 123, 22, 111, 18, 386, 21, 128, 1, 266, 72, 80, 448, 55, 1065, 42, 256, 1, 499, 101, 424, 281, 1725, 172, 3063, 86, 512, 1, 1037, 216, 1157, 1868, 1395, 6423, 575, 8624, 179

Offset

1,3

Comments

Table starts

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

...2..2...11...13....34.....65.....123......266......499.......1037........2042

...4..2...16....5....32.....22......72......101......216........486.........968

...8..3...47....7...111.....80.....424.....1157.....2922......12816.......33744

..16..6..147...18...448....281....1868.....6036....16344.....110672......332791

..32.10..386...55..1725...1395...11170....46215...142804....1296927.....3754619

..64.21.1065..172..6423...8756...55922...465040..1136003...19265064....60547641

.128.42.3063..575.24927..43128..291320..3509969..9080114..212347228...786789878

.256.86.8624.1962.96909.234170.1544411.29343177.73189971.2698247985.11028726211

Links

R. H. Hardin, Table of n, a(n) for n = 1..240

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 9]

k=4: [order 28] for n>32

k=5: [order 37] for n>41

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 19] for n>20

n=4: [order 61] for n>62

Example

Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..0. .0..0..1..0. .0..1..0..0. .0..0..1..1
..0..1..0..0. .0..1..0..0. .0..0..1..0. .0..1..0..0. .0..0..1..1
..1..1..1..0. .1..1..1..1. .1..1..1..1. .0..1..0..1. .0..1..1..0
..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..1..1
..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..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: A303325 A077901 A105619 * A302460 A303242 A302367

Adjacent sequences: A302209 A302210 A302211 * A302213 A302214 A302215

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 03 2018

Status

approved