A303254 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 49, 34, 0, 5, 146, 203, 250, 111, 0, 8, 537, 955, 1401, 1183, 361, 0, 13, 1934, 4556, 10264, 8664, 5918, 1172, 0, 21, 6861, 21843, 78679, 106803, 55624, 28680, 3809, 0, 34, 24386, 103319, 584333, 1218385, 1105676, 349273

Offset

1,5

Comments

Table starts

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

.0.....3.....14.......45........146.........537..........1934............6861

.0....11.....49......203........955........4556.........21843..........103319

.0....34....250.....1401......10264.......78679........584333.........4330427

.0...111...1183.....8664.....106803.....1218385......13529019.......153269484

.0...361...5918....55624....1105676....19457754.....322544617......5622650429

.0..1172..28680...349273...11394429...306224454....7600681910....204093228252

.0..3809.141255..2229806..118856245..4895684572..181926316054...7516309079483

.0.12377.691968.14141138.1230109648.77683246701.4319287740641.274539947294004

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 14]

k=4: [order 43] for n>44

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6

n=3: [order 19] for n>21

n=4: [order 63] for n>66

Example

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

Crossrefs

Column 2 is A180762.

Row 1 is A000045(n-1).

Row 2 is A302225.

Row 3 is A302473.

Row 4 is A302474.

Sequence in context: A302224 A302670 A302472 * A256068 A302381 A303102

Adjacent sequences: A303251 A303252 A303253 * A303255 A303256 A303257

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 20 2018

Status

approved