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%I #6 Sep 29 2013 03:36:12
%S 1,0,1,1,2,4,7
%N Take the standard 2-D lattice packing of pennies; a(n) = number of ways to pick n pennies (modulo rotations and reflections) such that the graph with nodes = centers of pennies, edges = pairs of touching pennies is connected and every edge belongs to at least one triangle.
%e Examples for n=3,4,5,6,7:
%e n=3:
%e ..o
%e .o.o
%e n=4:
%e ..o
%e .o.o
%e ..o
%e n=5:
%e ..o.o
%e .o.o.o
%e .
%e ....o
%e .o.o.o
%e ..o
%e n=6:
%e .o.o.o
%e o.o.o
%e .
%e ...o.o
%e o.o.o
%e .o
%e .
%e ...o
%e o.o.o
%e .o.o
%e .
%e ..o
%e .o.o
%e o.o.o
%e n=7:
%e ..o.o.o
%e .o.o.o.o
%e .
%e ..o.o
%e .o.o.o
%e ..o.o
%e .
%e ...o.o
%e ..o.o
%e .o.o.o
%e .
%e ....o.o
%e .o.o.o.o
%e ..o
%e .
%e ....o.o
%e ...o.o.o
%e ..o.o
%e .
%e ....o
%e .o.o.o.o
%e ..o...o
%e .
%e .....o.o
%e ..o.o.o
%e .o.o
%Y Cf. A171604.
%K nonn,more
%O 1,5
%A _N. J. A. Sloane_, Dec 17 2009
%E a(6) and a(7) corrected by _John W. Layman_, Dec 17 2009
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