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Take the standard 2-D lattice packing of pennies; a(n) = number of ways to pick n pennies (modulo rotations and reflections) such that if we form a linkage with centers of pennies as hinges and with struts between centers of two touching pennies, the linkage is rigid.
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%I #30 Nov 06 2016 08:56:48

%S 1,1,1,1,1,3,4

%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 if we form a linkage with centers of pennies as hinges and with struts between centers of two touching pennies, the linkage is rigid.

%C The pennies are laid flat on a horizontal plane. - _Daniel Forgues_, Oct 10 2016

%C We might have a rigid structure with a hole through which we have a taut chain of pennies (is this considered a packing?). - _Daniel Forgues_, Oct 08 2016

%e Examples for n=2,3,4,5,6,7:

%e n=2:

%e .o.o

%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 n=6:

%e .o.o.o

%e o.o.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

%e ..o.o

%Y Cf. A170807, A001524.

%K nonn,more

%O 1,6

%A _J. Lowell_, Dec 12 2009

%E Edited by _N. J. A. Sloane_, Dec 19 2009