A305281 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4 or 8 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, 1185, 2130, 684, 3076, 1, 1, 10444, 1932, 7433, 5060, 5060, 7433, 1932, 10444, 1, 1, 35480, 5308, 30191, 17335

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...1185....5060...17335....73058....275241....1135214

.1...272..256...2130...5060...26577...96739...437098...1790654....7846313

.1...908..684...7433..17335...96739..342596..1733499...7108688...34070865

.1..3076.1932..30191..73058..437098.1733499..9804507..44808093..246735199

.1.10444.5308.112815.275241.1790654.7108688.44808093.220905716.1340680187

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

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..0..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..0
..1..1..1..1. .0..1..1..0. .0..1..1..0. .1..0..0..0. .0..1..1..0
..1..1..0..0. .0..1..1..0. .1..1..1..1. .0..1..0..1. .0..1..1..0
..0..0..0..0. .1..1..1..0. .0..0..0..0. .1..1..1..0. .0..1..1..0
..1..0..1..1. .0..0..1..0. .0..0..0..0. .0..1..0..1. .1..0..1..0

Crossrefs

Column 2 is A303882.

Column 3 is A303883.

Column 4 is A303884.

Sequence in context: A296405 A174035 A303888 * A304894 A316576 A304551

Adjacent sequences: A305278 A305279 A305280 * A305282 A305283 A305284

Keyword

nonn,tabl

Author

R. H. Hardin, May 29 2018

Status

approved