A112580 Number of 3-D arrays of nonnegative integers with plane sums 2.

1, 12, 1152, 431424, 427723200, 920031955200, 3777894212198400, 27039993414897254400, 315084437077115278540800, 5667616936309704095784960000, 150796432741520745587273564160000

Offset

1,2

References

P. J. Cameron and T. W. Mueller, Decomposable functors and the exponential principle, II, in preparation

Links

Table of n, a(n) for n=1..11.

P. J. Cameron and T. W. Mueller, Decomposable functors and the exponential principle, II, arXiv:0911.3760 [math.CO]

Formula

a(n) = b(n) + Sum (k/n)*(n choose k)^3*b(k)*a(n-k), where b(n) counts indecomposable arrays (A112578 with first term 1).

Example

a(2)=12: eight 0-1 arrays and four with 2s at opposite vertices.

Crossrefs

Cf. A001499 (2-D case), A112578, A112579.

Sequence in context: A112457 A091782 A291952 * A229691 A180586 A178529

Adjacent sequences: A112577 A112578 A112579 * A112581 A112582 A112583

Keyword

nonn,easy

Author

Peter J. Cameron, Sep 14 2005

Status

approved