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A304775 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 21, 21, 8, 16, 49, 27, 49, 16, 32, 120, 67, 67, 120, 32, 64, 293, 139, 172, 139, 293, 64, 128, 719, 303, 443, 443, 303, 719, 128, 256, 1774, 685, 1094, 1581, 1094, 685, 1774, 256, 512, 4389, 1511, 2710, 5060, 5060, 2710, 1511, 4389, 512, 1024, 10893 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

...2....8...21....49....120.....293......719......1774.......4389.......10893

...4...21...27....67....139.....303......685......1511.......3316........7349

...8...49...67...172....443....1094.....2710......6861......17205.......43090

..16..120..139...443...1581....5060....15349.....50030.....160513......515542

..32..293..303..1094...5060...23872...100581....453229....2074725.....9305892

..64..719..685..2710..15349..100581...540901...3257711...19908669...116435693

.128.1774.1511..6861..50030..453229..3257711..26814986..224727491..1800071431

.256.4389.3316.17205.160513.2074725.19908669.224727491.2642187354.28890049643

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..364

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

k=4: [order 10] for n>13

k=5: [order 25] for n>28

k=6: [order 46] for n>50

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A303721.

Sequence in context: A303513 A303727 A305230 * A316518 A304472 A316289

Adjacent sequences:  A304772 A304773 A304774 * A304776 A304777 A304778

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 18 2018

STATUS

approved

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Last modified September 30 09:12 EDT 2022. Contains 357104 sequences. (Running on oeis4.)