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A299948 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 5
1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 27, 27, 69, 32, 64, 137, 47, 75, 47, 137, 64, 128, 301, 83, 191, 191, 83, 301, 128, 256, 705, 137, 401, 644, 401, 137, 705, 256, 512, 1461, 235, 952, 1604, 1604, 952, 235, 1461, 512, 1024, 3193, 412, 2258, 4924 (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

...2....7..13...29....69....137.....301......705......1461.......3193

...4...13..20...27....47.....83.....137......235.......412........709

...8...29..27...75...191....401.....952.....2258......5275......13250

..16...69..47..191...644...1604....4924....16163.....46665.....147161

..32..137..83..401..1604...4604...19269....79664....307083....1300811

..64..301.137..952..4924..19269..116051...642696...3313121...19431636

.128..705.235.2258.16163..79664..642696..5133698..34716313..275351726

.256.1461.412.5275.46665.307083.3313121.34716313.330723200.3594724687

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

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 17] for n>19

k=4: [order 67] for n>70

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A297883.

Column 3 is A299182.

Column 4 is A299183.

Sequence in context: A299388 A298494 A299187 * A298221 A299350 A299097

Adjacent sequences:  A299945 A299946 A299947 * A299949 A299950 A299951

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 22 2018

STATUS

approved

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Last modified September 21 19:55 EDT 2021. Contains 347598 sequences. (Running on oeis4.)