A261834 Number of n-step adjacent expansions on the hexagonal (honeycomb) lattice. Holes allowed.

1, 6, 48, 468, 5328, 68928, 994464, 15781920, 272594160, 5081825664

Offset

0,2

Comments

Initially only one cell C[0] is occupied on the lattice.

Then, for each i of (1..n), C[i] is chosen among the free cells adjacent to at least one of (C[0],...,C[i-1]).

a(n) is the number of distinct (C[1],...,C[n]).

Links

Table of n, a(n) for n=0..9.

Francois Alcover, tree.

Example

a(1) = 6 because a point has 6 neighbors on the hexagonal grid.
a(2) = 48 = a(1) * 8 because a two-cell group has 8 free neighbors.

Crossrefs

Cf. A007846 (same principle but on the rectangular lattice).

Cf. A001334.

Sequence in context: A365192 A365187 A319292 * A226740 A244509 A105627

Adjacent sequences: A261831 A261832 A261833 * A261835 A261836 A261837

Keyword

nonn,more,changed

Author

Francois Alcover, Mar 24 2016

Extensions

More terms from Francois Alcover, Apr 29 2016

Rephrasing and culling comments from Francois Alcover, Apr 29 2016

Added crossref to A007846 from Francois Alcover, May 01 2016

Status

approved