A296019 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 4 king-move neighboring 1s.

1, 2, 2, 3, 7, 3, 4, 13, 13, 4, 6, 28, 30, 28, 6, 9, 69, 91, 91, 69, 9, 13, 149, 280, 366, 280, 149, 13, 19, 330, 785, 1644, 1644, 785, 330, 19, 28, 755, 2319, 6545, 10703, 6545, 2319, 755, 28, 41, 1681, 6816, 26865, 58506, 58506, 26865, 6816, 1681, 41, 60, 3756, 19796

Offset

1,2

Comments

Table starts

..1....2.....3......4........6.........9.........13...........19............28

..2....7....13.....28.......69.......149........330..........755..........1681

..3...13....30.....91......280.......785.......2319.........6816.........19796

..4...28....91....366.....1644......6545......26865.......112345........461363

..6...69...280...1644....10703.....58506.....341979......2028843......11696474

..9..149...785...6545....58506....437195....3547681.....28921472.....229650211

.13..330..2319..26865...341979...3547681...40196846....459874052....5101988967

.19..755..6816.112345..2028843..28921472..459874052...7361110427..113693158171

.28.1681.19796.461363.11696474.229650211.5101988967.113693158171.2440444635515

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-3)

k=2: a(n) = a(n-1) +a(n-2) +4*a(n-3)

k=3: [order 10]

k=4: [order 21]

k=5: [order 55]

Example

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

Crossrefs

Column 1 is A000930(n+1).

Column 2 is A183435.

Sequence in context: A021451 A210188 A183442 * A134232 A123934 A208151

Adjacent sequences: A296016 A296017 A296018 * A296020 A296021 A296022

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 02 2017

Status

approved