%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