A301491 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 4, 5 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, 148, 148, 138, 32, 64, 383, 441, 599, 441, 383, 64, 128, 1063, 1372, 2354, 2354, 1372, 1063, 128, 256, 2951, 4326, 9415, 15124, 9415, 4326, 2951, 256, 512, 8193, 13641, 38558, 93753, 93753, 38558, 13641

Offset

1,2

Comments

Table starts

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

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

...4...18....52....148......441......1372........4326........13641

...8...50...148....599.....2354......9415.......38558.......158994

..16..138...441...2354....15124.....93753......594953......3838256

..32..383..1372...9415....93753....903707.....8479276.....81180752

..64.1063..4326..38558...594953...8479276...116648010...1642511178

.128.2951.13641.158994..3838256..81180752..1642511178..34593556316

.256.8193.42741.657238.24838061.782053062.23269383762.732289348979

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

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 89] for n>91.

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A280598.

Sequence in context: A300498 A300937 A300881 * A347940 A208269 A184761

Adjacent sequences: A301488 A301489 A301490 * A301492 A301493 A301494

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 22 2018

Status

approved