A298902 T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 3, 2, 2, 3, 0, 0, 5, 3, 4, 3, 5, 0, 0, 8, 7, 10, 10, 7, 8, 0, 0, 13, 12, 24, 32, 24, 12, 13, 0, 0, 21, 25, 56, 120, 120, 56, 25, 21, 0, 0, 34, 47, 142, 471, 963, 471, 142, 47, 34, 0, 0, 55, 96, 346, 2070, 4689, 4689, 2070, 346, 96, 55, 0, 0

Offset

1,12

Comments

Table starts

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

.0..1..1...2....3......5.......8........13.........21...........34

.0..1..1...2....3......7......12........25.........47...........96

.0..2..2...4...10.....24......56.......142........346..........874

.0..3..3..10...32....120.....471......2070.......9055........39809

.0..5..7..24..120....963....4689.....34739.....206363......1388386

.0..8.12..56..471...4689...44186....522001....5379458.....62969638

.0.13.25.142.2070..34739..522001...9994726..165198014...3059725754

.0.21.47.346.9055.206363.5379458.165198014.4485120457.138682695325

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +a(n-2)

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

k=4: [order 16]

k=5: [order 61]

Example

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

Crossrefs

Column 2 is A000045(n-1).

Sequence in context: A098356 A298167 A298957 * A298963 A180760 A233270

Adjacent sequences: A298899 A298900 A298901 * A298903 A298904 A298905

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 28 2018

Status

approved