A298727 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 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, 119, 230, 336, 230, 119, 253, 1, 1, 519, 285, 712, 1041, 1041, 712, 285, 519, 1, 1, 1018, 725, 2167, 3676, 4001, 3676, 2167, 725, 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.....119......285......725......1833.......4807

.1..18..15...34....77....230.....712.....2167.....6694.....20775......64197

.1..31..21...77...336...1041....3676....12970....45311....162322.....581460

.1..65..57..230..1041...4001...16320....67159...281930...1196239....5097819

.1.130.119..712..3676..16320...76983...380106..1892587...9597169...48598454

.1.253.285.2167.12970..67159..380106..2232433.13202628..79480110..477560387

.1.519.725.6694.45311.281930.1892587.13202628.92349689.659941442.4710349603

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 17] for n>18

k=4: [order 58] for n>60

Example

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

Crossrefs

Column 2 is A297937.

Sequence in context: A131404 A297943 A298554 * A299561 A298382 A299249

Adjacent sequences: A298724 A298725 A298726 * A298728 A298729 A298730

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 25 2018

Status

approved