A298195 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 26, 26, 8, 16, 88, 92, 88, 16, 32, 298, 354, 354, 298, 32, 64, 1012, 1385, 1609, 1385, 1012, 64, 128, 3440, 5450, 7629, 7629, 5450, 3440, 128, 256, 11700, 21362, 35969, 45143, 35969, 21362, 11700, 256, 512, 39804, 83805, 168880, 261255, 261255

Offset

1,2

Comments

Table starts

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

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

...4....26.....92.....354.....1385......5450......21362........83805

...8....88....354....1609.....7629.....35969.....168880.......794047

..16...298...1385....7629....45143....261255....1504330......8713831

..32..1012...5450...35969...261255...1863192...13176123.....93671028

..64..3440..21362..168880..1504330..13176123..114087318....992267592

.128.11700..83805..794047..8713831..93671028..992267592..10570868743

.256.39804.328854.3736043.50485951.666846880.8658476297.113136519433

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 17] for n>19

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A299942 A301841 A302069 * A299089 A299345 A299852

Adjacent sequences: A298192 A298193 A298194 * A298196 A298197 A298198

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 14 2018

Status

approved