A317271 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 13, 24, 1, 1, 82, 64, 64, 82, 1, 1, 272, 240, 498, 240, 272, 1, 1, 908, 842, 2922, 2922, 842, 908, 1, 1, 3076, 3302, 16877, 31878, 16877, 3302, 3076, 1, 1, 10444, 12740, 111073, 269286, 269286, 111073, 12740, 10444, 1, 1, 35480, 48468

Offset

1,5

Comments

Table starts

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

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

.1.....8....13......64.......240.........842.........3302..........12740

.1....24....64.....498......2922.......16877.......111073.........700859

.1....82...240....2922.....31878......269286......2915690.......29663556

.1...272...842...16877....269286.....3234635.....52389467......773668467

.1...908..3302..111073...2915690....52389467...1396521994....32539573668

.1..3076.12740..700859..29663556...773668467..32539573668..1165304769027

.1.10444.48468.4405884.295164308.11290705493.748729425556.40989107393702

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

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 20]

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

Example

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

Crossrefs

Column 2 is A303882.

Column 3 is A306131.

Column 4 is A306132.

Sequence in context: A304551 A316376 A306136 * A304419 A316244 A305954

Adjacent sequences: A317268 A317269 A317270 * A317272 A317273 A317274

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 25 2018

Status

approved