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.

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

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