A298575 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 4, 4, 1, 1, 8, 1, 8, 1, 1, 36, 2, 2, 36, 1, 1, 52, 14, 3, 14, 52, 1, 1, 100, 10, 41, 41, 10, 100, 1, 1, 356, 12, 38, 480, 38, 12, 356, 1, 1, 628, 72, 70, 374, 374, 70, 72, 628, 1, 1, 1220, 82, 374, 1055, 174, 1055, 374, 82, 1220, 1, 1, 3668, 90, 664, 9880, 604

Offset

1,5

Comments

Table starts

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

.1...4..4...8....36...52...100....356....628....1220.....3668......7268

.1...4..1...2....14...10....12.....72.....82......90......400.......600

.1...8..2...3....41...38....70....374....664....1327.....4668.....10974

.1..36.14..41...480..374..1055...9880..11792...31779...239375....376486

.1..52.10..38...374..174...604...5381...5527...16221...110018....190453

.1.100.12..70..1055..604..2888..28278..43961..164865..1297974...3202666

.1.356.72.374..9880.5381.28278.582062.684296.3320171.49103067..98469245

.1.628.82.664.11792.5527.43961.684296.939451.6179745.77845252.205903671

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)

k=3: a(n) = 7*a(n-3) +2*a(n-4) +a(n-5) -10*a(n-6) -2*a(n-7) -2*a(n-8) +2*a(n-9) with g.f. (1+3*x^2-8*x^3)/(1-x-8*x^3+4*x^4).

k=4: [order 32] for n>33

Example

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

Crossrefs

Sequence in context: A204028 A106314 A152716 * A326039 A183374 A176263

Adjacent sequences: A298572 A298573 A298574 * A298576 A298577 A298578

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 22 2018

Status

approved