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%I #11 Nov 14 2016 07:22:57
%S 1,4,108,12262,4938300,6591252334,28882229489388,430964179730348422,
%T 23569156965794642293500,5135577588131942706728912734,
%U 4693506649840749690490759617974508,18094001519512408937423329177374485400502,289589712516355625372445590522398228770148383420
%N Number of ways of placing any number of rods of length L into a LxLxL simple cubic lattice without any two rods intersecting.
%C The elements of this sequence are the row sums of A185697 (see that sequence for details). The values may be obtained by computing the values of the partition function f(L,1) given there for successive values of L.
%C The adjoining b-file lists all such values up to L=64.
%H Marcos Simoes, <a href="/A185702/b185702.txt">Table of n, a(n) for n = 0..64</a>
%F Z(L) = Sum_{a=0..L} Sum_{b=0..L} Sum_{c=0..L} ( binomial(L,a) * binomial(L,b) * binomial(L,c) * (2^(L-c)-1)^a * (2^(L-a)-1)^b * (2^(L-b)-1)^c ).
%t Unprotect[Power]; Power[0,0]=1; Protect[Power];
%t Z[L_]:=Sum[Binomial[L,a]*Binomial[L,b]*Binomial[L,c]*(2^(L-c)-1)^a*(2^(L-a)-1)^b*(2^(L-b)-1)^c,{a,0,L},{b,0,L},{c,0,L}]
%t Table[Z[L],{L,0,64}]
%Y Row sums of A185697.
%K nonn
%O 0,2
%A _Marcos Simoes_, Feb 10 2011
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