A306053 - OEIS

A306053

T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 21, 21, 8, 16, 49, 45, 49, 16, 32, 120, 142, 142, 120, 32, 64, 293, 439, 458, 439, 293, 64, 128, 719, 1261, 1962, 1962, 1261, 719, 128, 256, 1774, 3826, 6604, 12349, 6604, 3826, 1774, 256, 512, 4389, 11770, 22446, 66149, 66149, 22446, 11770

(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....45....142.....439......1261.......3826........11770.........35152

...8...49...142....458....1962......6604......22446........86464........311891

..16..120...439...1962...12349.....66149.....321707......1803281.......9990733

..32..293..1261...6604...66149....554682....3914486.....34263459.....301965791

..64..719..3826..22446..321707...3914486...36596835....458669749....5842600934

.128.1774.11770..86464.1803281..34263459..458669749...8395262149..162463649507

.256.4389.35152.311891.9990733.301965791.5842600934.162463649507.4973359586800

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 85] for n>89

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A303721.

Sequence in context: A316518 A304472 A316289 * A317230 A304310 A316209

Adjacent sequences: A306050 A306051 A306052 * A306054 A306055 A306056

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 18 2018

STATUS

approved