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A316209 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 78, 65, 16, 32, 192, 271, 271, 192, 32, 64, 569, 982, 1253, 982, 569, 64, 128, 1709, 3619, 5925, 5925, 3619, 1709, 128, 256, 5162, 13454, 28597, 36585, 28597, 13454, 5162, 256, 512, 15663, 50193, 139490, 232633, 232633 (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.....78.....271......982.......3619.......13454........50193

...8....65....271....1253.....5925......28597......139490.......684312

..16...192....982....5925....36585.....232633.....1494780......9661315

..32...569...3619...28597...232633....1962143....16731864....143845449

..64..1709..13454..139490..1494780...16731864...189577494...2170853960

.128..5162..50193..684312..9661315..143845449..2170853960..33224254530

.256.15663.187620.3366213.62645367.1242037097.24994758941.512094847931

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A304304.

Sequence in context: A306053 A317230 A304310 * A305776 A317125 A305593

Adjacent sequences:  A316206 A316207 A316208 * A316210 A316211 A316212

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 26 2018

STATUS

approved

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Last modified July 6 08:51 EDT 2020. Contains 335476 sequences. (Running on oeis4.)