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Number of n-step adjacent expansions on the hexagonal (honeycomb) lattice. Holes allowed.
1

%I #37 Apr 22 2024 21:44:52

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

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

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

%C 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]).

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

%H Francois Alcover, <a href="/A261834/a261834.png">tree</a>.

%e a(1) = 6 because a point has 6 neighbors on the hexagonal grid.

%e a(2) = 48 = a(1) * 8 because a two-cell group has 8 free neighbors.

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

%Y Cf. A001334.

%K nonn,more

%O 0,2

%A _Francois Alcover_, Mar 24 2016

%E More terms from _Francois Alcover_, Apr 29 2016

%E Rephrasing and culling comments from _Francois Alcover_, Apr 29 2016

%E Added crossref to A007846 from _Francois Alcover_, May 01 2016