A229917 Numbers of espalier polycubes of a given volume in dimension 4.

1, 4, 7, 16, 22, 46, 58, 107, 140, 227, 287, 464, 563, 851, 1067, 1530, 1866, 2661, 3198, 4428, 5361, 7185, 8613, 11524, 13639, 17839, 21272, 27359, 32300, 41369, 48512, 61311, 72105, 89904, 105226, 130834, 152164, 187297, 218356, 266444, 309125, 375995, 434670, 525045, 607329, 728256, 839874, 1004938

Offset

1,2

Comments

A (d+1)-pyramid polycube is a (d+1)-polycube obtained by gluing together horizontal (d+1)-plateaux (parallelepipeds of height 1) in such a way that the cell (0,0,...,0) belongs to the first plateau and each cell with coordinates (0,n_1,...,n_d) belonging to the first plateau is such that n_1 , ... , n_d >= 0.

If the cell with coordinates (n_0,n_1,...,n_d) belongs to the (n_0+1)-st plateau (n_0>0), then the cell with coordinates (n_0-1, n_1, ... ,n_d) belongs to the n_0-th plateau.

A (d+1)-espalier is a (d+1)-pyramid such that each plateau contains the cell (n_0,0,...,0).

Links

Table of n, a(n) for n=1..48.

Crossrefs

Cf. A229915, A227925.

Sequence in context: A325657 A054599 A285998 * A095755 A245937 A348771

Adjacent sequences: A229914 A229915 A229916 * A229918 A229919 A229920

Keyword

nonn

Author

Matthieu Deneufchâtel, Oct 03 2013

Status

approved