A303888 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3 or 4 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 11, 24, 1, 1, 82, 36, 36, 82, 1, 1, 272, 87, 166, 87, 272, 1, 1, 908, 256, 487, 487, 256, 908, 1, 1, 3076, 684, 2130, 1150, 2130, 684, 3076, 1, 1, 10444, 1932, 7433, 4964, 4964, 7433, 1932, 10444, 1, 1, 35480, 5308, 30191, 16431

Offset

1,5

Comments

Table starts

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

.1.....4....8.....24.....82.....272.....908.....3076.....10444.....35480

.1.....8...11.....36.....87.....256.....684.....1932......5308.....14809

.1....24...36....166....487....2130....7433....30191....112815....444834

.1....82...87....487...1150....4964...16431....68704....254498...1032541

.1...272..256...2130...4964...24985...88901...384168...1517262...6387363

.1...908..684...7433..16431...88901..308271..1437397...5832957..25738579

.1..3076.1932..30191..68704..384168.1437397..7577931..32153502.162027971

.1.10444.5308.112815.254498.1517262.5832957.32153502.148783767.818391800

Links

R. H. Hardin, Table of n, a(n) for n = 1..263

Formula

Empirical for column k:

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

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

k=3: [order 16] for n>18

k=4: [order 38] for n>41

Example

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

Crossrefs

Sequence in context: A332307 A296405 A174035 * A305281 A304894 A316576

Adjacent sequences: A303885 A303886 A303887 * A303889 A303890 A303891

Keyword

nonn,tabl

Author

R. H. Hardin, May 02 2018

Status

approved