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

Author

Francois Alcover, Mar 24 2016

Keywords

• nonn
• more

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]).

Examples

			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.
		

Links

• Francois Alcover, tree.

Crossrefs

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

Cf. A001334.

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