A195739 Triangle read by rows: DX(n,d) = number of properly d-dimensional polyominoes with n cells, modulo translations (n>=1, 0 <= d <= n-1).

1, 0, 1, 0, 1, 4, 0, 1, 17, 32, 0, 1, 61, 348, 400, 0, 1, 214, 2836, 8640, 6912, 0, 1, 758, 21225, 129288, 254800, 153664, 0, 1, 2723, 154741, 1688424, 6160640, 8749056, 4194304, 0, 1, 9908, 1123143, 20762073, 125055400, 313921008, 343901376, 136048896

Offset

1,6

Comments

According to Barequet-Barequet-Rote, p. 261, the value DX(7, 6) = 134209 given by W. F. Lunnon is incorrect; it should be 153664, see A127670. - Alexander Knapp, May 13 2013

Links

Robert A. Russell, Table of n, a(n) for n = 1..60

R. Barequet, G. Barequet, and G. Rote, Formulae and growth rates of high-dimensional polycubes, Combinatorica 30 (2010), pp. 257-275.

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

Example

Triangle begins with DX(1,0):
n\d 0  1   2     3      4      5      6
---------------------------------------
1...1
2...0  1
3...0  1   4
4...0  1  17    32
5...0  1  61   348    400
6...0  1 214  2836   8640   6912
7...0  1 758 21225 129288 254800 153664
...

Crossrefs

Columns give A006762, A006763, A006764. Cf. A195738, A049430.

Diagonals (with formulas) are A127670, A171860, A191092, A259015, A290738.

Sequence in context: A189355 A221817 A054375 * A323128 A334703 A259938

Adjacent sequences: A195736 A195737 A195738 * A195740 A195741 A195742

Keyword

nonn,tabl

Author

N. J. A. Sloane, Sep 23 2011

Status

approved