A316883 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 37, 28, 16, 32, 94, 105, 105, 94, 32, 64, 284, 388, 452, 388, 284, 64, 128, 752, 1280, 2401, 2401, 1280, 752, 128, 256, 2244, 4121, 11532, 18847, 11532, 4121, 2244, 256, 512, 6532, 13933, 54613, 125218, 125218, 54613

Offset

1,2

Comments

Table starts

...1....2.....4.......8.......16.........32..........64...........128

...2....4....14......28.......94........284.........752..........2244

...4...14....37.....105......388.......1280........4121.........13933

...8...28...105.....452.....2401......11532.......54613........268142

..16...94...388....2401....18847.....125218......843479.......6198339

..32..284..1280...11532...125218....1187727....11791971.....128278641

..64..752..4121...54613...843479...11791971...180224021....3018929955

.128.2244.13933..268142..6198339..128278641..3018929955...79732305036

.256.6532.46641.1322178.45184963.1404259002.51534776482.2144543383081

Links

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

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 15] for n>17

k=4: [order 61] for n>63

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304341.

Sequence in context: A317036 A305911 A317153 * A317611 A220461 A220287

Adjacent sequences: A316880 A316881 A316882 * A316884 A316885 A316886

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 15 2018

Status

approved