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A049429 Triangle T(n,d) = number of distinct d-dimensional polyominoes (or polycubes) with n cells (0 < d < n). 11
1, 1, 1, 1, 4, 2, 1, 11, 11, 3, 1, 34, 77, 35, 6, 1, 107, 499, 412, 104, 11, 1, 368, 3442, 4888, 2009, 319, 23, 1, 1284, 24128, 57122, 36585, 8869, 951, 47, 1, 4654, 173428, 667959, 647680, 231574, 36988, 2862, 106, 1, 17072, 1262464, 7799183, 11173880, 5712765, 1297366, 146578, 8516, 235 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,5

COMMENTS

These are unoriented polyominoes of the regular tilings with Schläfli symbols {oo}, {4,4}, {4,3,4}, {4,3,3,4}, etc. Each tile is a regular orthotope (hypercube). For unoriented polyominoes, chiral pairs are counted as one. The dimension of the convex hull of the cell centers determines the dimension d. - Robert A. Russell, Aug 09 2022

REFERENCES

Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

LINKS

Table of n, a(n) for n=2..56.

R. C. Schroeppel, A few mathematical experiments

EXAMPLE

From Robert A. Russell, Aug 09 2022: (Start)

Triangle begins with T(2,1):

n\d 1     2       3       4        5       6       7      8    9  10

2   1

3   1     1

4   1     4       2

5   1    11      11       3

6   1    34      77      35        6

7   1   107     499     412      104      11

8   1   368    3442    4888     2009     319      23

9   1  1284   24128   57122    36585    8869     951     47

10  1  4654  173428  667959   647680  231574   36988   2862  106

11  1 17072 1262464 7799183 11173880 5712765 1297366 146578 8516 235

(End)

CROSSREFS

Cf. A049430 (col. d=0 added), A195738 (oriented), A195739 (fixed).

Diagonals (with algorithms) are A000055, A036364, A355053.

Row sums give A005519. Columns are A006765-A006768.

Sequence in context: A342088 A193607 A075397 * A328647 A183158 A174005

Adjacent sequences:  A049426 A049427 A049428 * A049430 A049431 A049432

KEYWORD

nonn,nice,tabl,hard

AUTHOR

Richard C. Schroeppel

EXTENSIONS

Two more rows added by Robert A. Russell, Aug 09 2022.

STATUS

approved

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Last modified October 5 14:03 EDT 2022. Contains 357258 sequences. (Running on oeis4.)