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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
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
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 A363365
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 02 2017
STATUS
approved