A317611 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 38, 28, 16, 32, 94, 109, 109, 94, 32, 64, 284, 419, 472, 419, 284, 64, 128, 752, 1413, 2639, 2639, 1413, 752, 128, 256, 2244, 4708, 13134, 23031, 13134, 4708, 2244, 256, 512, 6532, 16406, 64593, 161091, 161091, 64593

Offset

1,2

Comments

Table starts

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

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

...4...14....38.....109......419.......1413........4708.........16406

...8...28...109.....472.....2639......13134.......64593........329236

..16...94...419....2639....23031.....161091.....1160029.......8965243

..32..284..1413...13134...161091....1624676....17100005.....193630364

..64..752..4708...64593..1160029...17100005...271661553....4668181991

.128.2244.16406..329236..8965243..193630364..4668181991..124728567511

.256.6532.56424.1675126.67933591.2178634452.80648172452.3358612290228

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304341.

Sequence in context: A305911 A317153 A316883 * A220461 A220287 A354492

Adjacent sequences: A317608 A317609 A317610 * A317612 A317613 A317614

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 01 2018

Status

approved