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A296019 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 4 king-move neighboring 1s. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)