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A305769 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 30, 30, 8, 16, 112, 141, 112, 16, 32, 420, 684, 684, 420, 32, 64, 1576, 3282, 4893, 3282, 1576, 64, 128, 5912, 15874, 34001, 34001, 15874, 5912, 128, 256, 22176, 76613, 240701, 332676, 240701, 76613, 22176, 256, 512, 83184, 370087 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

...2.....8......30......112........420.........1576..........5912

...4....30.....141......684.......3282........15874.........76613

...8...112.....684.....4893......34001.......240701.......1696681

..16...420....3282....34001.....332676......3343997......33584061

..32..1576...15874...240701....3343997.....47791549.....686168124

..64..5912...76613..1696681...33584061....686168124...14187207394

.128.22176..370087.11974403..336821283...9812796379..291309897184

.256.83184.1787161.84503446.3382396016.140721354959.6009246932279

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) = 4*a(n-1) -2*a(n-2) +4*a(n-3)

k=3: [order 11]

k=4: [order 35] for n>37

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A281949.

Sequence in context: A303469 A281955 A316183 * A317118 A305530 A317004

Adjacent sequences:  A305766 A305767 A305768 * A305770 A305771 A305772

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 10 2018

STATUS

approved

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Last modified September 19 13:07 EDT 2021. Contains 347557 sequences. (Running on oeis4.)