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A281955 T(n,k)=Number of nXk 0..1 arrays with no element unequal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards. 8
1, 2, 2, 4, 8, 4, 8, 30, 30, 8, 16, 112, 133, 112, 16, 32, 420, 587, 587, 420, 32, 64, 1576, 2559, 3389, 2559, 1576, 64, 128, 5912, 11251, 19089, 19089, 11251, 5912, 128, 256, 22176, 49293, 111354, 130416, 111354, 49293, 22176, 256, 512, 83184, 216274 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1......2.......4.........8.........16..........32............64

...2......8......30.......112........420........1576..........5912

...4.....30.....133.......587.......2559.......11251.........49293

...8....112.....587......3389......19089......111354........640778

..16....420....2559.....19089.....130416......944967.......6763599

..32...1576...11251....111354.....944967.....8606584......77540974

..64...5912...49293....640778....6763599....77540974.....882270370

.128..22176..216274...3716432...48984359...705601833...10123006858

.256..83184..948407..21502354..354789627..6439770627..116604534792

.512.312032.4159753.124531091.2573699813.58888042279.1345813812696

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..219

FORMULA

Empirical for column k:

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

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

k=3: [order 10] for n>12

k=4: [order 28] for n>32

k=5: [order 69] for n>73

EXAMPLE

Some solutions for n=4 k=4

..0..1..1..0. .0..0..0..1. .0..1..0..0. .0..0..0..1. .0..1..0..0

..1..1..1..1. .1..1..1..1. .0..1..1..1. .0..0..0..0. .1..1..1..0

..1..1..1..0. .1..1..1..1. .1..1..1..1. .0..1..1..1. .0..1..1..1

..1..1..1..0. .0..1..1..1. .0..1..1..1. .1..1..1..1. .0..1..0..0

CROSSREFS

Column 1 is A000079(n-1).

Sequence in context: A302965 A302808 A303469 * A316183 A305769 A317118

Adjacent sequences:  A281952 A281953 A281954 * A281956 A281957 A281958

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 03 2017

STATUS

approved

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Last modified July 30 04:28 EDT 2021. Contains 346348 sequences. (Running on oeis4.)