A305523 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 219, 128, 16, 32, 512, 1482, 1482, 512, 32, 64, 2048, 10082, 16480, 10082, 2048, 64, 128, 8192, 68603, 186237, 186237, 68603, 8192, 128, 256, 32768, 466858, 2102155, 3536750, 2102155, 466858, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

...2......8.......32........128..........512...........2048..............8192

...4.....32......219.......1482........10082..........68603............466858

...8....128.....1482......16480.......186237........2102155..........23747613

..16....512....10082.....186237......3536750.......66949063........1269418258

..32...2048....68603....2102155.....66949063.....2122076804.......67425576120

..64...8192...466858...23747613...1269418258....67425576120.....3592436519091

.128..32768..3177374..268359015..24080732454..2143769629842...191577652761963

.256.131072.21625010.3032800805.456869647792.68172646692968.10218588450186728

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)

k=3: a(n) = 6*a(n-1) +8*a(n-2) -10*a(n-3) -44*a(n-4) -30*a(n-5) for n>6

k=4: [order 15] for n>17

k=5: [order 58] for n>59

Example

Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..1
..1..1..0..1. .1..1..1..1. .0..0..1..0. .1..1..0..1. .0..1..1..0
..0..1..1..0. .1..1..1..0. .0..0..1..1. .1..1..1..1. .1..1..0..0
..1..1..0..0. .0..1..0..0. .1..0..0..1. .1..1..1..0. .0..0..0..1
..0..1..0..0. .1..0..0..1. .0..1..0..1. .1..0..0..0. .0..0..1..1

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A299746 A299668 A300259 * A298970 A316960 A299740

Adjacent sequences: A305520 A305521 A305522 * A305524 A305525 A305526

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 04 2018

Status

approved