A049430 Triangle read by rows: T(n,d) is the number of distinct properly d-dimensional polyominoes (or polycubes) with n cells (n >= 1, d >= 0).

1, 0, 1, 0, 1, 1, 0, 1, 4, 2, 0, 1, 11, 11, 3, 0, 1, 34, 77, 35, 6, 0, 1, 107, 499, 412, 104, 11, 0, 1, 368, 3442, 4888, 2009, 319, 23, 0, 1, 1284, 24128, 57122, 36585, 8869, 951, 47, 0, 1, 4654, 173428, 667959, 647680, 231574, 36988, 2862, 106, 0, 1, 17072, 1262464, 7799183, 11173880, 5712765, 1297366, 146578, 8516, 235

Offset

1,9

Links

Table of n, a(n) for n=1..66.

W. F. Lunnon, Counting multidimensional polyominoes. Computer Journal 18 (1975), no. 4, pp. 366-367.

Example

Triangle begins:
1
0 1
0 1     1
0 1     4       2
0 1    11      11       3
0 1    34      77      35        6
0 1   107     499     412      104      11
0 1   368    3442    4888     2009     319      23
0 1  1284   24128   57122    36585    8869     951     47
0 1  4654  173428  667959   647680  231574   36988   2862  106
0 1 17072 1262464 7799183 11173880 5712765 1297366 146578 8516 235
...

Crossrefs

Cf. A049429 (col. d=0 omitted), A195738 (oriented), A195739 (fixed).

Row sums give A005519. Columns give A006765, A006766, A006767, A006768.

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

Cf. A330891 (cumulative sums of the rows).

Sequence in context: A088393 A121225 A216715 * A055356 A297331 A028956

Adjacent sequences: A049427 A049428 A049429 * A049431 A049432 A049433

Keyword

nonn,nice,tabl,hard

Author

Richard C. Schroeppel

Extensions

Edited by N. J. A. Sloane, Sep 23 2011

More terms from John Niss Hansen, Mar 31 2015

Status

approved