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A305776 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 81, 65, 16, 32, 192, 292, 292, 192, 32, 64, 569, 1096, 1481, 1096, 569, 64, 128, 1709, 4172, 7528, 7528, 4172, 1709, 128, 256, 5162, 15953, 38623, 51586, 38623, 15953, 5162, 256, 512, 15663, 61111, 199257, 362200, 362200 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

...2.....8.....23......65.......192........569........1709..........5162

...4....23.....81.....292......1096.......4172.......15953.........61111

...8....65....292....1481......7528......38623......199257.......1028731

..16...192...1096....7528.....51586.....362200.....2553685......18030904

..32...569...4172...38623....362200....3492739....33891076.....329477646

..64..1709..15953..199257...2553685...33891076...453853629....6095547869

.128..5162..61111.1028731..18030904..329477646..6095547869..113299205109

.256.15663.234288.5312551.127390570.3206311981.81987206051.2110390711467

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

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

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

k=3: [order 16]

k=4: [order 57] for n>59

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A304304.

Sequence in context: A317230 A304310 A316209 * A317125 A305593 A317011

Adjacent sequences:  A305773 A305774 A305775 * A305777 A305778 A305779

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 10 2018

STATUS

approved

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Last modified August 19 18:30 EDT 2022. Contains 356229 sequences. (Running on oeis4.)