A299249 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 18, 6, 18, 1, 1, 31, 18, 18, 31, 1, 1, 65, 30, 55, 30, 65, 1, 1, 130, 87, 192, 192, 87, 130, 1, 1, 253, 202, 652, 1095, 652, 202, 253, 1, 1, 519, 526, 2002, 5042, 5042, 2002, 526, 519, 1, 1, 1018, 1449, 6741, 21251, 35320, 21251, 6741, 1449

Offset

1,5

Comments

Table starts

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

.1...5....7....18.....31.......65.......130........253..........519

.1...7....6....18.....30.......87.......202........526.........1449

.1..18...18....55....192......652......2002.......6741........23631

.1..31...30...192...1095.....5042.....21251.....111818.......577544

.1..65...87...652...5042....35320....223750....1634125.....12440063

.1.130..202..2002..21251...223750...2044405...21212789....227105938

.1.253..526..6741.111818..1634125..21212789..321811361...4948662848

.1.519.1449.23631.577544.12440063.227105938.4948662848.111378069579

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5

k=3: [order 19] for n>20

k=4: [order 72] for n>73

Example

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

Crossrefs

Column 2 is A297937.

Sequence in context: A298727 A299561 A298382 * A299458 A300096 A379621

Adjacent sequences: A299246 A299247 A299248 * A299250 A299251 A299252

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 05 2018

Status

approved