A297866 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 4 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 5, 4, 5, 0, 0, 10, 13, 13, 10, 0, 0, 25, 62, 15, 62, 25, 0, 0, 54, 222, 233, 233, 222, 54, 0, 0, 125, 820, 1052, 2621, 1052, 820, 125, 0, 0, 282, 3159, 5774, 21519, 21519, 5774, 3159, 282, 0, 0, 641, 11882, 36119, 174970, 284344, 174970

Offset

1,8

Comments

Table starts

.0...0.....0......0........0.........0...........0.............0..............0

.0...1.....2......5.......10........25..........54...........125............282

.0...2.....4.....13.......62.......222.........820..........3159..........11882

.0...5....13.....15......233......1052........5774.........36119.........204522

.0..10....62....233.....2621.....21519......174970.......1556367.......13214094

.0..25...222...1052....21519....284344.....3740362......52727368......711614693

.0..54...820...5774...174970...3740362....76517448....1699781649....36000744495

.0.125..3159..36119..1556367..52727368..1699781649...58344517697..1923723833047

.0.282.11882.204522.13214094.711614693.36000744495.1923723833047.99045666327382

Links

R. H. Hardin, Table of n, a(n) for n = 1..197

Formula

Empirical for column k:

k=1: a(n) =

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

k=3: [order 14] for n>16

k=4: [order 47] for n>50

Example

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

Crossrefs

Sequence in context: A330619 A245693 A370374 * A298133 A298070 A298719

Adjacent sequences: A297863 A297864 A297865 * A297867 A297868 A297869

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 07 2018

Status

approved