A299561 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 18, 5, 18, 1, 1, 31, 15, 15, 31, 1, 1, 65, 21, 34, 21, 65, 1, 1, 130, 57, 77, 77, 57, 130, 1, 1, 253, 121, 230, 348, 230, 121, 253, 1, 1, 519, 289, 734, 1094, 1094, 734, 289, 519, 1, 1, 1018, 747, 2261, 3919, 4315, 3919, 2261, 747, 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...5...15....21.....57.....121......289.......747......1901.......5017

.1..18..15...34....77....230.....734.....2261......7050.....22143......69461

.1..31..21...77...348...1094....3919....13977.....49728....182756.....669766

.1..65..57..230..1094...4315...18032....75491....325547...1416774....6187701

.1.130.121..734..3919..18032...88551...451972...2321249..12137569...63355517

.1.253.289.2261.13977..75491..451972..2753155..16947296.105906482..660212203

.1.519.747.7050.49728.325547.2321249.16947296.124402861.927664758.6913834651

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

k=3: [order 19] for n>20

k=4: [order 72] for n>73

Example

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

Crossrefs

Column 2 is A297937.

Sequence in context: A297943 A298554 A298727 * A298382 A299249 A299458

Adjacent sequences: A299558 A299559 A299560 * A299562 A299563 A299564

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 12 2018

Status

approved