The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A229924

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A229924

Numbers of pyramid polycubes of a given volume in dimension 5.
(history; published version)

#15 by N. J. A. Sloane at Sun Oct 13 10:16:44 EDT 2013

STATUS

editing

approved

#14 by N. J. A. Sloane at Sun Oct 13 10:16:40 EDT 2013

NAME

Numbers of pyramid polycubes of a given volume in dimension 5.

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

CROSSREFS

Cf. A229914, A227926.

STATUS

proposed

editing

#13 by Matthieu Deneufchâtel at Sat Oct 12 06:06:28 EDT 2013

STATUS

editing

proposed

#12 by Matthieu Deneufchâtel at Sat Oct 12 06:06:24 EDT 2013

CROSSREFS

A229914,A227926

#11 by Matthieu Deneufchâtel at Fri Oct 04 11:46:36 EDT 2013

COMMENTS

A (d+1)-pyramid polycube is a (d+1)-polycube obtained by gluing together vertical horizontal (d+1)-plateaus plateaux (parallelepiped parallelepipeds of height 1) in such a way that

the cell (0,0,...,0) belongs to the first plateau and each cell of coordinate with coordinates (0,n_1,...,n_d) belonging to the first plateau is such that n_1 , ... , n_d >= 0.

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

Discussion

Fri Oct 11

18:13

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#10 by T. D. Noe at Fri Oct 04 11:11:52 EDT 2013

STATUS

proposed

editing

#9 by Matthieu Deneufchâtel at Fri Oct 04 10:59:19 EDT 2013

STATUS

editing

proposed

#8 by Matthieu Deneufchâtel at Fri Oct 04 10:57:01 EDT 2013

COMMENTS

A $(d+1)$-\emph{pyramid} polycube is a $(d+1)$-polycube obtained by gluing together vertical $(d+1)$-plateaus (parallelepiped of height 1) in such a way that

\begin{itemize}

\item the cell $(0,0,\dots,...,0)$ belongs to the first plateau and each cell of coordinate $(0,n_1,\dots,...,n_d)$ belonging to the first plateau is such that n_1 , ... , n_d >= 0.

$if the cell of coordinates (n_0,n_1,...,n_d) belongs to the (n_0+1)-th plateau (n_0>0), then the cell of coordinates (n_0-1, n_1,\dots, ... ,n_d\geq ) belongs to the n_0$-th plateau.

\item If the cell of coordinates $(n_0,n_1,\dots,n_d)$ belongs to the $(n_0+1)$-th plateau ($n_0>0$),

then the cell of coordinates $(n_0-1, n_1,\dots,n_d)$) belongs to the $n_0$-th plateau.

\end{itemize}

#7 by Joerg Arndt at Fri Oct 04 09:00:57 EDT 2013

STATUS

proposed

editing

#6 by Matthieu Deneufchâtel at Fri Oct 04 06:06:49 EDT 2013

STATUS

editing

proposed