A296313 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 3 or 6 king-move neighboring 1s.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 4, 1, 1, 6, 7, 7, 6, 1, 1, 9, 13, 10, 13, 9, 1, 1, 13, 23, 23, 23, 23, 13, 1, 1, 19, 37, 45, 68, 45, 37, 19, 1, 1, 28, 63, 76, 162, 162, 76, 63, 28, 1, 1, 41, 109, 150, 343, 479, 343, 150, 109, 41, 1, 1, 60, 183, 293, 864, 1198, 1198, 864, 293, 183

Offset

1,5

Comments

Table starts

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

.1..2...3...4....6.....9....13.....19......28......41.......60........88

.1..3...5...7...13....23....37.....63.....109.....183......309.......527

.1..4...7..10...23....45....76....150.....293.....532.....1010......1942

.1..6..13..23...68...162...343....864....2075....4715....11332.....27032

.1..9..23..45..162...479..1198...3534...10374...28464....80600....233023

.1.13..37..76..343..1198..3300..11494...40212..124949...411819...1420725

.1.19..63.150..864..3534.11494..49634..205982..764169..3069413..12612285

.1.28.109.293.2075.10374.40212.205982.1039840.4709965.22551308.113142176

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

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

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

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

k=5: [order 50]

Example

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

Crossrefs

Column 2 is A000930(n+1).

Column 3 is A003229.

Sequence in context: A306697 A297845 A183456 * A183342 A046688 A208342

Adjacent sequences: A296310 A296311 A296312 * A296314 A296315 A296316

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 10 2017

Status

approved