A221828 T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns

0, 0, 0, 0, 3, 0, 0, 16, 14, 0, 0, 73, 202, 64, 0, 0, 333, 2879, 2930, 292, 0, 0, 1519, 40983, 115417, 41618, 1332, 0, 0, 6929, 583419, 4715043, 4755445, 592601, 6076, 0, 0, 31607, 8304016, 192788993, 570066685, 194407111, 8434490, 27716, 0, 0, 144177

Offset

1,5

Comments

Table starts

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

.0......3.........16...........73...........333...........1519..........6929

.0.....14........202.........2879.........40983.........583419.......8304016

.0.....64.......2930.......115417.......4715043......192788993....7888216533

.0....292......41618......4755445.....570066685....68573607669.8233561918895

.0...1332.....592601....194407111...68489860450.24121109763712

.0...6076....8434490...7954432829.8224749361083

.0..27716..120053263.325446165881

.0.126428.1708776751

.0.576708

.0

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical for col 2: a(n) = 5*a(n-1) -2*a(n-2) for n>3

Empirical for row 2: a(k)=5*a(k-1)-2*a(k-2) for k>4

Example

Some solutions for n=3 k=4
..0..1..1..0....1..2..1..1....1..1..0..2....0..2..0..1....1..1..1..1
..1..2..0..1....1..1..2..1....2..1..1..1....2..1..0..1....1..0..1..2
..2..1..2..1....0..0..1..1....1..1..1..0....1..2..1..1....1..1..2..0

Crossrefs

Column 2 is A060801(n-1)

Sequence in context: A278208 A105786 A291802 * A368348 A278188 A101192

Adjacent sequences: A221825 A221826 A221827 * A221829 A221830 A221831

Keyword

nonn,tabl

Author

R. H. Hardin Jan 26 2013

Status

approved