A305911 T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 35, 28, 16, 32, 94, 98, 98, 94, 32, 64, 284, 358, 396, 358, 284, 64, 128, 752, 1124, 2075, 2075, 1124, 752, 128, 256, 2244, 3534, 9140, 15460, 9140, 3534, 2244, 256, 512, 6532, 11667, 40412, 86944, 86944, 40412, 11667, 6532

Offset

1,2

Comments

Table starts

...1....2.....4......8.......16........32.........64.........128...........256

...2....4....14.....28.......94.......284........752........2244..........6532

...4...14....35.....98......358......1124.......3534.......11667.........37816

...8...28....98....396.....2075......9140......40412......189729........873060

..16...94...358...2075....15460.....86944.....505624.....3261562......20076871

..32..284..1124...9140....86944....595490....4408093....36427606.....282035936

..64..752..3534..40412...505624...4408093...42789430...473649265....4825821471

.128.2244.11667.189729..3261562..36427606..473649265..7157370110...96982248284

.256.6532.37816.873060.20076871.282035936.4825821471.96982248284.1710658272713

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

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 > 16;

k=4: [order 69] for n > 70.

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304341.

Sequence in context: A316218 A305642 A317036 * A317153 A316883 A317611

Adjacent sequences: A305908 A305909 A305910 * A305912 A305913 A305914

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 14 2018

Status

approved