A305954 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 23, 24, 1, 1, 82, 107, 107, 82, 1, 1, 272, 537, 959, 537, 272, 1, 1, 908, 2800, 8433, 8433, 2800, 908, 1, 1, 3076, 14652, 76951, 126733, 76951, 14652, 3076, 1, 1, 10444, 77128, 705763, 1969026, 1969026, 705763, 77128, 10444, 1

Offset

1,5

Comments

Table starts

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

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

.1.....8.....23......107........537..........2800...........14652

.1....24....107......959.......8433.........76951..........705763

.1....82....537.....8433.....126733.......1969026........30700722

.1...272...2800....76951....1969026......52618569......1406191296

.1...908..14652...705763...30700722....1406191296.....64233268442

.1..3076..77128..6501334..480588948...37746118432...2949134027463

.1.10444.406622.59966772.7529843048.1013991166787.135468194522667

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 16] for n>17

k=4: [order 49] for n>51

Example

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

Crossrefs

Column 2 is A303882.

Sequence in context: A317271 A304419 A316244 * A317215 A305685 A317065

Adjacent sequences: A305951 A305952 A305953 * A305955 A305956 A305957

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 15 2018

Status

approved