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A261834
Number of n-step adjacent expansions on the hexagonal (honeycomb) lattice. Holes allowed.
1
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
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: A365187 A378155 A319292 * A226740 A244509 A105627
KEYWORD
nonn,more
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