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A305593 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 95, 65, 16, 32, 192, 390, 390, 192, 32, 64, 569, 1626, 2451, 1626, 569, 64, 128, 1709, 6818, 14746, 14746, 6818, 1709, 128, 256, 5162, 28530, 89466, 126484, 89466, 28530, 5162, 256, 512, 15663, 119266, 544280, 1103744 (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.....95......390......1626........6818.........28530.........119266

...8....65....390.....2451.....14746.......89466........544280........3314595

..16...192...1626....14746....126484.....1103744.......9637513.......84163172

..32...569...6818....89466...1103744....13941521.....175683720.....2213918787

..64..1709..28530...544280...9637513...175683720....3190446497....57940960729

.128..5162.119266..3314595..84163172..2213918787...57940960729..1517186100046

.256.15663.498890.20186517.735136189.27910555993.1053163229940.39781453968523

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] for n>17

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

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A304304.

Sequence in context: A316209 A305776 A317125 * A317011 A316876 A317604

Adjacent sequences:  A305590 A305591 A305592 * A305594 A305595 A305596

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 05 2018

STATUS

approved

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Last modified May 7 15:02 EDT 2021. Contains 343650 sequences. (Running on oeis4.)