A299581 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 10, 2, 1, 1, 5, 10, 10, 5, 1, 1, 9, 27, 19, 27, 9, 1, 1, 22, 63, 43, 43, 63, 22, 1, 1, 45, 115, 126, 172, 126, 115, 45, 1, 1, 101, 267, 327, 616, 616, 327, 267, 101, 1, 1, 218, 569, 860, 1734, 2597, 1734, 860, 569, 218, 1, 1, 477, 1193, 2401

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..10...10....27.....63.....115......267........569........1193

.1...2..10...19....43....126.....327......860.......2401........6733

.1...5..27...43...172....616....1734.....6188......22944.......81842

.1...9..63..126...616...2597...10646....56122.....291690.....1619418

.1..22.115..327..1734..10646...61273...464681....3999592....35862058

.1..45.267..860..6188..56122..464681..6245870...83493860..1154724040

.1.101.569.2401.22944.291690.3999592.83493860.1821672943.40042035336

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) +3*a(n-2) -2*a(n-4) for n>5

k=3: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -4*a(n-4) -2*a(n-5) -2*a(n-6) +a(n-9) for n>13

k=4: [order 34]

Example

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

Crossrefs

Column 2 is A052962(n-2).

Sequence in context: A100078 A051242 A234934 * A069287 A215749 A102775

Adjacent sequences: A299578 A299579 A299580 * A299582 A299583 A299584

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 13 2018

Status

approved