A299852 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 26, 26, 8, 16, 88, 93, 88, 16, 32, 298, 357, 357, 298, 32, 64, 1012, 1401, 1626, 1401, 1012, 64, 128, 3440, 5533, 7770, 7770, 5533, 3440, 128, 256, 11700, 21764, 36968, 46799, 36968, 21764, 11700, 256, 512, 39804, 85620, 175258, 276154, 276154

Offset

1,2

Comments

Table starts

...1.....2......4.......8.......16........32..........64..........128

...2.....8.....26......88......298......1012........3440........11700

...4....26.....93.....357.....1401......5533.......21764........85620

...8....88....357....1626.....7770.....36968......175258.......831558

..16...298...1401....7770....46799....276154.....1620056......9548178

..32..1012...5533...36968...276154...2030211....14789406....108058244

..64..3440..21764..175258..1620056..14789406...133388471...1204666013

.128.11700..85620..831558..9548178.108058244..1204666013..13452150161

.256.39804.336966.3948404.56314168.790761211.10910971094.150810121407

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) +2*a(n-3) -6*a(n-4) -4*a(n-5)

k=3: [order 16] for n>18

k=4: [order 64] for n>66

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298189.

Sequence in context: A298195 A299089 A299345 * A299008 A299675 A299753

Adjacent sequences: A299849 A299850 A299851 * A299853 A299854 A299855

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2018

Status

approved