A300372 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 3, 3, 3, 3, 0, 0, 2, 3, 3, 3, 2, 0, 0, 6, 8, 4, 4, 8, 6, 0, 0, 6, 16, 22, 32, 22, 16, 6, 0, 0, 11, 32, 39, 92, 92, 39, 32, 11, 0, 0, 16, 70, 102, 270, 366, 270, 102, 70, 16, 0, 0, 22, 135, 298, 1262, 1592, 1592, 1262, 298, 135, 22, 0, 0, 37, 293

Offset

1,17

Comments

Table starts

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

.0..1..1...1....3.....2......6.......6.......11........16..........22

.0..1..0...3....3.....8.....16......32.......70.......135.........293

.0..1..3...3....4....22.....39.....102......298.......833........2105

.0..3..3...4...32....92....270....1262.....3561.....13976.......48859

.0..2..8..22...92...366...1592....6925....36101....161645......762469

.0..6.16..39..270..1592..12042...75739...490425...3084820....19634393

.0..6.32.102.1262..6925..75739..729062..5841423..53750463...469053654

.0.11.70.298.3561.36101.490425.5841423.70536528.833035233.10021999204

Links

R. H. Hardin, Table of n, a(n) for n = 1..263

Formula

Empirical for column k:

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

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

k=3: [order 14]

k=4: [order 43] for n>45

Example

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

Crossrefs

Column 2 is A062200(n-2).

Sequence in context: A227827 A033700 A122916 * A132973 A107760 A180560

Adjacent sequences: A300369 A300370 A300371 * A300373 A300374 A300375

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 04 2018

Status

approved