A297915 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 12, 12, 1, 1, 37, 10, 37, 1, 1, 104, 49, 49, 104, 1, 1, 301, 144, 268, 144, 301, 1, 1, 864, 481, 1281, 1281, 481, 864, 1, 1, 2485, 2016, 6044, 10809, 6044, 2016, 2485, 1, 1, 7144, 7730, 35788, 86201, 86201, 35788, 7730, 7144, 1, 1, 20541, 30637

Offset

1,5

Comments

Table starts

.1....1.....1.......1........1..........1............1.............1

.1....5....12......37......104........301..........864..........2485

.1...12....10......49......144........481.........2016..........7730

.1...37....49.....268.....1281.......6044........35788........202419

.1..104...144....1281....10809......86201.......789026.......6952444

.1..301...481....6044....86201....1084333.....15983426.....223362153

.1..864..2016...35788...789026...15983426....362523451....7903384843

.1.2485..7730..202419..6952444..223362153...7903384843..267640924872

.1.7144.30637.1185261.62368324.3195010015.176308045666.9307023743602

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 5*a(n-2) +8*a(n-3) +4*a(n-4)

k=3: [order 13] for n>15

k=4: [order 50] for n>53

Example

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

Crossrefs

Sequence in context: A174861 A110522 A146987 * A298508 A298328 A299221

Adjacent sequences: A297912 A297913 A297914 * A297916 A297917 A297918

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 08 2018

Status

approved