A296674 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 2 or 3 king-move neighboring 1s.

2, 3, 3, 5, 10, 5, 8, 25, 25, 8, 13, 68, 82, 68, 13, 21, 208, 334, 334, 208, 21, 34, 609, 1451, 2295, 1451, 609, 34, 55, 1785, 5938, 16541, 16541, 5938, 1785, 55, 89, 5375, 25144, 110036, 213800, 110036, 25144, 5375, 89, 144, 16174, 108174, 775010, 2358963

Offset

1,1

Links

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

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 3*a(n-1) +5*a(n-3) -10*a(n-4) -12*a(n-5) -4*a(n-6)

k=3: [order 12]

k=4: [order 27]

k=5: [order 67]

Example

Table starts
..2.....3......5........8.........13...........21.............34
..3....10.....25.......68........208..........609...........1785
..5....25.....82......334.......1451.........5938..........25144
..8....68....334.....2295......16541.......110036.........775010
.13...208...1451....16541.....213800......2358963.......28341757
.21...609...5938...110036....2358963.....40937523......794602323
.34..1785..25144...775010...28341757....794602323....25499216805
.55..5375.108174..5466936..346828018..15702927104...833656369935
.89.16174.463106.38297415.4150012532.301022037125.26222808591554
...
Some solutions for n=4 k=4
..1..1..1..0. .0..0..0..0. .0..1..1..0. .0..1..0..0. .0..0..1..1
..1..0..0..1. .1..0..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..1
..1..0..1..0. .0..0..0..0. .0..0..0..0. .1..0..0..1. .1..1..1..0
..1..1..0..0. .1..0..0..1. .1..0..0..1. .1..1..0..0. .1..0..0..0

Crossrefs

Column 1 is A000045(n+2).

Sequence in context: A175147 A001180 A228778 * A297073 A019460 A329057

Adjacent sequences: A296671 A296672 A296673 * A296675 A296676 A296677

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 18 2017

Status

approved