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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. 8
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 (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....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

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Last modified February 3 04:55 EST 2023. Contains 360024 sequences. (Running on oeis4.)