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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 03:10 EDT 2021. Contains 348073 sequences. (Running on oeis4.)