A298775 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 25, 25, 23, 5, 8, 49, 47, 78, 47, 49, 8, 13, 99, 109, 233, 233, 109, 99, 13, 21, 189, 245, 779, 682, 779, 245, 189, 21, 34, 383, 545, 2359, 2603, 2603, 2359, 545, 383, 34, 55, 777, 1253, 7024, 11657, 11320, 11657, 7024

Offset

1,5

Comments

Table starts

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

..1...3....7....13.....23......49.......99.......189........383.........777

..1...7...15....25.....47.....109......245.......545.......1253........2859

..2..13...25....78....233.....779.....2359......7024......21572.......66763

..3..23...47...233....682....2603....11657.....39908.....149791......617528

..5..49..109...779...2603...11320....61333....284618....1376511.....6959439

..8..99..245..2359..11657...61333...484813...2887678...18497464...127977516

.13.189..545..7024..39908..284618..2887678..22160831..186728055..1683257109

.21.383.1253.21572.149791.1376511.18497464.186728055.2093453587.24925712914

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) +a(n-2)

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

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

k=4: [order 62] for n>65

Example

Some solutions for n=6 k=5
..0..0..0..1..0. .0..1..0..0..0. .0..1..1..1..0. .0..0..0..0..0
..1..0..0..0..1. .1..0..0..0..1. .1..0..0..0..1. .1..0..0..0..1
..0..1..1..1..0. .0..1..1..1..0. .1..0..0..0..1. .0..1..1..1..0
..0..1..1..1..0. .0..1..1..1..0. .1..0..0..0..1. .0..1..1..1..0
..0..1..1..1..0. .0..1..1..1..0. .0..1..1..1..0. .0..1..1..1..0
..1..0..0..0..1. .1..0..0..0..1. .1..1..1..0..1. .1..0..0..0..1

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297953.

Column 3 is A297954.

Column 4 is A297955.

Sequence in context: A298660 A299612 A297959 * A298582 A299574 A298396

Adjacent sequences: A298772 A298773 A298774 * A298776 A298777 A298778

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 26 2018

Status

approved