A298444 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 11, 2, 1, 1, 5, 2, 2, 5, 1, 1, 9, 27, 7, 27, 9, 1, 1, 22, 36, 34, 34, 36, 22, 1, 1, 45, 86, 105, 214, 105, 86, 45, 1, 1, 101, 162, 406, 1270, 1270, 406, 162, 101, 1, 1, 218, 368, 1504, 3963, 10681, 3963, 1504, 368, 218, 1, 1, 477, 727, 6183

Offset

1,12

Comments

Table starts

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

.1...1...1....2......5.......9........22.........45..........101...........218

.1...1..11....2.....27......36........86........162..........368...........727

.1...2...2....7.....34.....105.......406.......1504.........6183.........25013

.1...5..27...34....214....1270......3963......22290.......109407........575051

.1...9..36..105...1270...10681.....72509.....692536......6184710......57152783

.1..22..86..406...3963...72509....610525....9392919....119508030....1732328018

.1..45.162.1504..22290..692536...9392919..240137045...5101146140..120394407026

.1.101.368.6183.109407.6184710.119508030.5101146140.176490627544.6773268608554

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) -2*a(n-4) for n>5

k=3: [order 12] for n>13

k=4: [order 34] for n>36

Example

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

Crossrefs

Column 2 is A052962(n-2).

Sequence in context: A353877 A250221 A365610 * A224480 A037299 A329941

Adjacent sequences: A298441 A298442 A298443 * A298445 A298446 A298447

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 19 2018

Status

approved