A304472 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 21, 21, 8, 16, 49, 41, 49, 16, 32, 120, 117, 117, 120, 32, 64, 293, 316, 322, 316, 293, 64, 128, 719, 810, 1100, 1100, 810, 719, 128, 256, 1774, 2208, 2957, 5063, 2957, 2208, 1774, 256, 512, 4389, 6012, 8254, 18879, 18879, 8254, 6012, 4389

Offset

1,2

Comments

Table starts

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

...2....8....21....49.....120......293......719......1774.......4389

...4...21....41...117.....316......810.....2208......6012......15837

...8...49...117...322....1100.....2957.....8254.....26698......77788

..16..120...316..1100....5063....18879....68338....289227....1157258

..32..293...810..2957...18879....89071...380640...2075796...10775870

..64..719..2208..8254...68338...380640..1802240..12149499...76809028

.128.1774..6012.26698..289227..2075796.12149499.101407827..820468158

.256.4389.15837.77788.1157258.10775870.76809028.820468158.8813328376

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

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

k=4: [order 21] for n>25

k=5: [order 84] for n>88

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A303721.

Sequence in context: A305230 A304775 A316518 * A316289 A306053 A317230

Adjacent sequences: A304469 A304470 A304471 * A304473 A304474 A304475

Keyword

nonn,tabl

Author

R. H. Hardin, May 13 2018

Status

approved