A296990 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 3, 4 or 5 king-move neighboring 1s.

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 14, 7, 1, 1, 14, 28, 28, 14, 1, 1, 33, 98, 74, 98, 33, 1, 1, 77, 447, 440, 440, 447, 77, 1, 1, 185, 1653, 2514, 5487, 2514, 1653, 185, 1, 1, 460, 6507, 12601, 65694, 65694, 12601, 6507, 460, 1, 1, 1148, 27374, 71009, 639327, 1621832

Offset

1,5

Comments

Table starts

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

.1...2.....4......7.......14..........33...........77.............185

.1...4....14.....28.......98.........447.........1653............6507

.1...7....28.....74......440........2514........12601...........71009

.1..14....98....440.....5487.......65694.......639327.........7181983

.1..33...447...2514....65694.....1621832.....26724927.......546305423

.1..77..1653..12601...639327....26724927....702794334.....24416753991

.1.185..6507..71009..7181983...546305423..24416753991...1529176981800

.1.460.27374.401521.81977832.11821168013.892243428330.100472530942946

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) = 2*a(n-1) +a(n-2) +3*a(n-3) -4*a(n-4) -2*a(n-5) -4*a(n-6)

k=3: [order 20]

k=4: [order 43]

Example

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

Crossrefs

Sequence in context: A104382 A086629 A203948 * A156184 A056588 A126770

Adjacent sequences: A296987 A296988 A296989 * A296991 A296992 A296993

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 22 2017

Status

approved