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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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 11 03:41 EDT 2022. Contains 356046 sequences. (Running on oeis4.)