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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 16:40 EDT 2021. Contains 348155 sequences. (Running on oeis4.)