A305245 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 18, 24, 16, 32, 64, 32, 32, 64, 32, 64, 184, 86, 94, 86, 184, 64, 128, 432, 158, 273, 273, 158, 432, 128, 256, 1088, 343, 767, 1134, 767, 343, 1088, 256, 512, 2944, 721, 2128, 3288, 3288, 2128, 721, 2944, 512, 1024, 7360, 1520

Offset

1,2

Comments

Table starts

...1....2....4.....8.....16......32......64......128.......256........512

...2....4...12....24.....64.....184.....432.....1088......2944.......7360

...4...12...18....32.....86.....158.....343......721......1520.......3228

...8...24...32....94....273.....767....2128.....6150.....17387......49477

..16...64...86...273...1134....3288...11731....39986....136448.....468584

..32..184..158...767...3288...12521...55039...238455...1028982....4474894

..64..432..343..2128..11731...55039..311014..1742187...9652212...54215925

.128.1088..721..6150..39986..238455.1742187.12726939..91021791..667854447

.256.2944.1520.17387.136448.1028982.9652212.91021791.841464188.8000379451

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5) for n>6

k=3: [order 8] for n>11

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

k=5: [order 34] for n>42

k=6: [order 98] for n>104

Example

Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..1
..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..1..0. .1..1..1..1
..1..0..1..1. .0..0..0..0. .1..0..0..1. .0..0..0..0. .1..1..1..1
..0..1..1..1. .0..1..0..0. .0..0..0..1. .0..0..0..0. .1..1..1..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..0..1

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A303794.

Sequence in context: A320196 A033740 A303800 * A304479 A316304 A304848

Adjacent sequences: A305242 A305243 A305244 * A305246 A305247 A305248

Keyword

nonn,tabl

Author

R. H. Hardin, May 28 2018

Status

approved