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.

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

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