A298957 T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 3, 2, 2, 3, 0, 0, 5, 3, 4, 3, 5, 0, 0, 8, 5, 6, 6, 5, 8, 0, 0, 13, 8, 11, 10, 11, 8, 13, 0, 0, 21, 13, 18, 22, 22, 18, 13, 21, 0, 0, 34, 21, 31, 47, 102, 47, 31, 21, 34, 0, 0, 55, 34, 53, 143, 390, 390, 143, 53, 34, 55, 0, 0, 89, 55, 91, 418, 1990

Offset

1,12

Comments

Table starts

.0..0..0..0...0....0......0.......0........0..........0...........0

.0..1..1..2...3....5......8......13.......21.........34..........55

.0..1..1..2...3....5......8......13.......21.........34..........55

.0..2..2..4...6...11.....18......31.......53.........91.........156

.0..3..3..6..10...22.....47.....143......418.......1449........4821

.0..5..5.11..22..102....390....1990.....8875......42338......200422

.0..8..8.18..47..390...3101...21928...156972....1153968.....8497555

.0.13.13.31.143.1990..21928..300849..3354122...43052414...516822488

.0.21.21.53.418.8875.156972.3354122.54865647.1090267927.19403449274

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) +a(n-2)

k=3: a(n) = a(n-1) +a(n-2)

k=4: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) -2*a(n-5) +a(n-6) +a(n-7)

k=5: [order 69]

Example

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

Crossrefs

Columns 2 and 3 are A000045(n-1).

Column 4 is A298163.

Sequence in context: A298183 A098356 A298167 * A298902 A298963 A180760

Adjacent sequences: A298954 A298955 A298956 * A298958 A298959 A298960

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 30 2018

Status

approved