A185702 Number of ways of placing any number of rods of length L into a LxLxL simple cubic lattice without any two rods intersecting.

1, 4, 108, 12262, 4938300, 6591252334, 28882229489388, 430964179730348422, 23569156965794642293500, 5135577588131942706728912734, 4693506649840749690490759617974508, 18094001519512408937423329177374485400502, 289589712516355625372445590522398228770148383420

Offset

0,2

Comments

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.

The adjoining b-file lists all such values up to L=64.

Links

Marcos Simoes, Table of n, a(n) for n = 0..64

Formula

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 ).

Mathematica

Unprotect[Power]; Power[0, 0]=1; Protect[Power];
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}]
Table[Z[L], {L, 0, 64}]

Crossrefs

Row sums of A185697.

Sequence in context: A061464 A107048 A269187 * A279046 A212803 A002109

Adjacent sequences: A185699 A185700 A185701 * A185703 A185704 A185705

Keyword

nonn

Author

Marcos Simoes, Feb 10 2011

Status

approved