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A296674 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 2 or 3 king-move neighboring 1s. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 27 11:47 EDT 2022. Contains 354097 sequences. (Running on oeis4.)