A317215 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5, 7 or 8 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, 127358, 76951, 14652, 3076, 1, 1, 10444, 77128, 705763, 1987026, 1987026, 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.....127358.......1987026........31138620

.1...272...2800....76951....1987026......53479785......1441577878

.1...908..14652...705763...31138620....1441577878.....66735041323

.1..3076..77128..6501334..489866621...39018757534...3103003384185

.1.10444.406622.59966772.7714180199.1057115569193.144406060742969

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

Crossrefs

Column 2 is A303882.

Column 3 is A305949.

Column 4 is A305950.

Sequence in context: A304419 A316244 A305954 * A305685 A317065 A316932

Adjacent sequences: A317212 A317213 A317214 * A317216 A317217 A317218

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 23 2018

Status

approved