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.

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

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