A298589 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 9, 2, 1, 1, 5, 5, 5, 5, 1, 1, 9, 16, 4, 16, 9, 1, 1, 22, 31, 13, 13, 31, 22, 1, 1, 45, 28, 31, 65, 31, 28, 45, 1, 1, 101, 87, 83, 233, 233, 83, 87, 101, 1, 1, 218, 125, 262, 441, 1112, 441, 262, 125, 218, 1, 1, 477, 185, 819, 1765, 4620, 4620, 1765

Offset

1,12

Comments

Table starts

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

.1...1...1...2....5......9......22.......45........101.........218..........477

.1...1...9...5...16.....31......28.......87........125.........185..........418

.1...2...5...4...13.....31......83......262........819........2690.........8887

.1...5..16..13...65....233.....441.....1765.......7431.......28212.......121244

.1...9..31..31..233...1112....4620....29589.....169601.....1004366......6170528

.1..22..28..83..441...4620...26343...240692....2382399....22651784....228684042

.1..45..87.262.1765..29589..240692..3833927...54266663...764702068..11301659452

.1.101.125.819.7431.169601.2382399.54266663.1239155011.27405626123.629168904793

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

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 9] for n>13

k=4: [order 34]

Example

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

Crossrefs

Column 2 is A052962(n-2).

Sequence in context: A365637 A249270 A153739 * A272286 A019645 A011065

Adjacent sequences: A298586 A298587 A298588 * A298590 A298591 A298592

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 22 2018

Status

approved