A049429 - OEIS

A049429

Triangle T(n,d) = number of distinct d-dimensional polyominoes (or polycubes) with n cells (0 < d < n).

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: A193607 A358735 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