A301906 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 1, 4, 1, 2, 1, 8, 1, 2, 3, 1, 16, 1, 3, 2, 7, 1, 32, 1, 6, 2, 5, 16, 1, 64, 1, 10, 7, 8, 10, 43, 1, 128, 1, 21, 12, 40, 12, 26, 117, 1, 256, 1, 42, 27, 96, 92, 64, 65, 330, 1, 512, 1, 86, 62, 316, 320, 532, 196, 170, 935, 1, 1024, 1, 179, 160, 1078, 1588, 1934, 1999, 864, 442

Offset

1,3

Comments

Table starts

...1.1...1...1....1.....1......1.......1........1..........1...........1

...2.1...2...2....3.....6.....10......21.......42.........86.........179

...4.1...3...2....2.....7.....12......27.......62........160.........387

...8.1...7...5....8....40.....96.....316.....1078.......3831.......13331

..16.1..16..10...12....92....320....1588.....7234......34477......171770

..32.1..43..26...64...532...1934...14860....86638.....568382.....4029337

..64.1.117..65..196..1999...8781..104732...770376....7398173....75183520

.128.1.330.170..864.10150..49709..952467..8263384..113474387..1620307756

.256.1.935.442.3236.46226.253844.7931939.81388360.1622304450.32687652025

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

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

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

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

k=5: a(n) = 4*a(n-1) +5*a(n-2) -20*a(n-3) -4*a(n-4) +16*a(n-5) for n>6

k=6: [order 20] for n>21

k=7: [order 30] for n>33

Empirical for row n:

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

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

n=3: [order 30] for n>31

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 4 is A245306(n-1).

Row 2 is A240513(n-3).

Sequence in context: A226174 A208482 A199856 * A302150 A193554 A372701

Adjacent sequences: A301903 A301904 A301905 * A301907 A301908 A301909

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 28 2018

Status

approved