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A331621
Number of distinct structures that can be made from n cubes without overhangs.
1
1, 1, 2, 4, 12, 35, 129, 495, 2101, 9154, 41356, 189466, 880156, 4120515, 19425037
OFFSET
0,3
COMMENTS
This is an extension of the free polyominoes (A000105) to the third dimension. Structures are considered equivalent if they can be mapped into each other by reflection in a vertical plane or rotation around the vertical axis. They are not equivalent if they can only be mapped onto each other by rotation around an axis parallel to the horizontal plane.
LINKS
Arnauld Chevallier, Javascript Node.JS program
Nicholas A. Kennedy, Buildings made from cubes, Code Golf Stack Exchange 2020
EXAMPLE
For n = 0, one (the empty) structure is possible.
For n = 1, only one structure is possible, a single cube.
For n = 2, two structures are possible: two cubes one on top of the other, and two next to each other.
For n = 3, four structures are possible: an L shape with the L oriented vertically, an L shape with the L laid flat, a structure with 3 cubes stacked on top of each other and a structure with 3 cubes laid flat.
For n = 4, there are 12 possible distinct structures made from 4 cubes without overhangs. These include 1 structure that is 4 cubes tall, 1 structure that is 3 cubes tall, 5 structures that are 2 cubes tall and 5 that are 1 cube tall.
PROG
(JavaScript) See Arnauld Chevallier link
(Java) See Miles link
CROSSREFS
Extension to the third dimension of A000105.
Sequence in context: A019447 A148206 A148207 * A334250 A211768 A112083
KEYWORD
nonn,more
AUTHOR
Nicholas A. Kennedy, Jan 22 2020
STATUS
approved