A297943 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 18, 4, 18, 1, 1, 31, 14, 14, 31, 1, 1, 65, 16, 33, 16, 65, 1, 1, 130, 51, 74, 74, 51, 130, 1, 1, 253, 102, 226, 330, 226, 102, 253, 1, 1, 519, 258, 694, 1032, 1032, 694, 258, 519, 1, 1, 1018, 667, 2121, 3640, 3977, 3640, 2121, 667, 1018, 1

Offset

1,5

Comments

Table starts

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

.1...5...7...18....31.....65.....130......253......519......1018.......2055

.1...7...4...14....16.....51.....102......258......667......1716.......4557

.1..18..14...33....74....226.....694.....2121.....6517.....20208......62318

.1..31..16...74...330...1032....3640....12800....44663....159995.....572956

.1..65..51..226..1032...3977...16198....66625...279485...1186383....5055084

.1.130.102..694..3640..16198...76374...376126..1869918...9484034...48011978

.1.253.258.2121.12800..66625..376126..2200020.12989533..78218401..469760261

.1.519.667.6517.44663.279485.1869918.12989533.90659562.647989857.4623257850

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

k=3: [order 16] for n>17

k=4: [order 57] for n>59

Example

Some solutions for n=7 k=4
..0..0..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..1..1..0
..0..1..1..0. .1..0..1..0. .1..1..1..0. .0..1..1..0. .1..1..0..0
..1..0..0..0. .1..1..0..0. .1..0..1..0. .0..1..0..1. .0..1..1..1
..0..1..1..1. .1..0..1..0. .1..0..0..0. .0..1..0..1. .1..1..0..1
..0..0..1..0. .0..1..0..1. .1..1..1..0. .0..0..1..1. .1..0..1..0
..1..0..1..1. .0..1..0..1. .0..0..0..1. .1..1..1..0. .1..0..0..1
..0..0..0..1. .0..0..1..1. .1..0..1..1. .1..0..1..1. .1..1..1..1

Crossrefs

Sequence in context: A132737 A137754 A131404 * A298554 A298727 A299561

Adjacent sequences: A297940 A297941 A297942 * A297944 A297945 A297946

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 09 2018

Status

approved