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

Author

Peter J. Cameron, Sep 14 2005

Keywords

• nonn
• easy

Examples

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

References

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

Links

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

Crossrefs

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

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).