A300937 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 18, 18, 8, 16, 50, 52, 50, 16, 32, 138, 143, 143, 138, 32, 64, 383, 412, 505, 412, 383, 64, 128, 1063, 1225, 1534, 1534, 1225, 1063, 128, 256, 2951, 3699, 4781, 6220, 4781, 3699, 2951, 256, 512, 8193, 11243, 15292, 21787, 21787, 15292, 11243

Offset

1,2

Comments

Table starts

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

...2....7....18.....50.....138.....383.....1063......2951.......8193

...4...18....52....143.....412....1225.....3699.....11243......34012

...8...50...143....505....1534....4781....15292.....48838.....158036

..16..138...412...1534....6220...21787....77434....287515....1062023

..32..383..1225...4781...21787...97745...399796...1701284....7433503

..64.1063..3699..15292...77434..399796..2038646...9872494...49173493

.128.2951.11243..48838..287515.1701284..9872494..57179007..324488769

.256.8193.34012.158036.1062023.7433503.49173493.324488769.2175995920

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) -a(n-2) +a(n-3) +a(n-4) -2*a(n-5) -a(n-6)

k=3: [order 24] for n>25

k=4: [order 95] for n>96

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A280598.

Column 3 is A300493.

Sequence in context: A280604 A301323 A300498 * A300881 A301491 A347940

Adjacent sequences: A300934 A300935 A300936 * A300938 A300939 A300940

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 16 2018

Status

approved