A318024 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 6, 4, 8, 14, 14, 8, 16, 35, 45, 35, 16, 32, 95, 133, 133, 95, 32, 64, 257, 419, 569, 419, 257, 64, 128, 700, 1382, 2227, 2227, 1382, 700, 128, 256, 1907, 4495, 9063, 12039, 9063, 4495, 1907, 256, 512, 5202, 14754, 37030, 60157, 60157, 37030, 14754, 5202

Offset

1,2

Comments

Table starts

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

...2....6....14.....35......95.......257........700........1907.........5202

...4...14....45....133.....419......1382.......4495.......14754........48525

...8...35...133....569....2227......9063......37030......153117.......634563

..16...95...419...2227...12039.....60157.....304184.....1569163......8067785

..32..257..1382...9063...60157....400016....2495323....16110625....103827789

..64..700..4495..37030..304184...2495323...20241433...163342483...1322465254

.128.1907.14754.153117.1569163..16110625..163342483..1699138124..17279766046

.256.5202.48525.634563.8067785.103827789.1322465254.17279766046.223853493247

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) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -2*a(n-4) -a(n-6) +a(n-7)

k=3: [order 18] for n>23

k=4: [order 70] for n>74

Example

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

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A317764 A318075 A318343 * A320409 A096466 A088965

Adjacent sequences: A318021 A318022 A318023 * A318025 A318026 A318027

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 12 2018

Status

approved