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A297889 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 king-move adjacent elements, with upper left element zero. 8
1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 26, 26, 69, 32, 64, 137, 41, 36, 41, 137, 64, 128, 301, 67, 84, 84, 67, 301, 128, 256, 705, 99, 134, 114, 134, 99, 705, 256, 512, 1461, 156, 223, 162, 162, 223, 156, 1461, 512, 1024, 3193, 255, 396, 248, 253, 248 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1....2...4...8..16..32..64.128..256..512.1024..2048..4096..8192..16384

...2....7..13..29..69.137.301.705.1461.3193.7373.15729.34405.78569.170813

...4...13..20..26..41..67..99.156..255..406..654..1075..1765..2903...4816

...8...29..26..36..84.134.223.396..638.1173.2157..3812..6922.12304..21936

..16...69..41..84.114.162.248.368..520..786.1308..2126..3136..5052...7740

..32..137..67.134.162.253.264.437..656..942.1308..2254..3113..4698...7376

..64..301..99.223.248.264.433.579..650.1124.1469..2441..3648..5209...7873

.128..705.156.396.368.437.579.734..864.1154.1711..2267..3028..4060...5423

.256.1461.255.638.520.656.650.864.1037.1248.1647..2362..2966..3994...5228

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..1104

FORMULA

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n>6

k=3: [order 10] for n>11

k=4: [order 30] for n>34

k=5: [order 86] for n>91

EXAMPLE

Some solutions for n=7 k=4

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

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

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Sequence in context: A220308 A203975 A270246 * A298294 A299388 A298494

Adjacent sequences:  A297886 A297887 A297888 * A297890 A297891 A297892

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 07 2018

STATUS

approved

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Last modified December 9 09:37 EST 2021. Contains 349627 sequences. (Running on oeis4.)