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Number of fixed 3D piled polyominoes: polycubes with fixed orientation, with no cubes "sitting on air".
0

%I #6 Mar 31 2012 13:21:29

%S 1,3,11,44,184,792,3484,15592,70745,324561,1502511,7007929,32892778,

%T 155221536,735915652,3503270920,16737092549,80218277681,385574074383,

%U 1858059853316,8974761939239,43441619693731,210682920968681

%N Number of fixed 3D piled polyominoes: polycubes with fixed orientation, with no cubes "sitting on air".

%F a(n) = sum_{m=1}^n A001168(m)*C(n-1, m-1). If both sequences are shifted left, binomial transform of A001168.

%e For n = 4, there are 4 orientations of the angled tricube excluded: those which set it on a point; this leaves 8 orientations of the angled tricube and 3 of the straight tricube.

%Y Cf. A001168, A001931 (fixed polycubes).

%K nonn

%O 1,2

%A _Franklin T. Adams-Watters_, Oct 15 2005

%E Corrected by Franklin T. Adams-Watters, Oct 25 2006