A296115 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 3 or 4 king-move neighboring 1s.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 8, 9, 9, 8, 1, 1, 17, 26, 16, 26, 17, 1, 1, 31, 74, 64, 64, 74, 31, 1, 1, 71, 163, 185, 503, 185, 163, 71, 1, 1, 166, 535, 528, 2800, 2800, 528, 535, 166, 1, 1, 365, 1735, 2109, 14057, 29003, 14057, 2109, 1735, 365, 1, 1, 856, 4960

Offset

1,5

Comments

Table starts

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

.1...2....3....4......8.......17........31..........71...........166

.1...3....6....9.....26.......74.......163.........535..........1735

.1...4....9...16.....64......185.......528........2109..........7336

.1...8...26...64....503.....2800.....14057......106920........726414

.1..17...74..185...2800....29003....197661.....2401049......28504534

.1..31..163..528..14057...197661...1993970....34228975.....553395326

.1..71..535.2109.106920..2401049..34228975..1061506422...28707285600

.1.166.1735.7336.726414.28504534.553395326.28707285600.1365762093736

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: [order 11]

k=4: [order 27]

k=5: [order 89]

Example

Some solutions for n=6 k=4
..0..1..1..0. .0..1..1..0. .0..1..0..0. .0..0..0..0. .0..0..1..0
..0..1..1..0. .0..1..1..0. .1..1..1..0. .0..1..1..0. .0..1..1..1
..0..0..0..0. .0..0..0..0. .0..1..0..0. .0..1..1..0. .0..0..1..0
..1..1..0..0. .0..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..1
..1..1..0..0. .1..1..1..0. .0..0..1..1. .0..1..1..0. .0..0..1..1
..0..0..0..0. .0..1..0..0. .0..0..0..0. .0..1..1..0. .0..0..1..1

Crossrefs

Sequence in context: A034328 A034253 A203952 * A118687 A281587 A026022

Adjacent sequences: A296112 A296113 A296114 * A296116 A296117 A296118

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 04 2017

Status

approved