A006763 -id:A006763 - cp's OEIS frontend

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

N. J. A. Sloane, Sep 23 2011

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

			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
...

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.

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

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

A006764 Number of fixed properly-4-dimensional polyominoes with n cells.

Original entry on oeis.org

0, 0, 0, 0, 400, 8640, 129288, 1688424, 20762073, 248384816, 2937307716, 34618858308

Offset: 1

N. J. A. Sloane

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

W. F. Lunnon, Counting Multidimensional Polyominoes, Computer Journal, Vol. 18 (1975), pp. 366-67.

Cf. A000105. A column of A195739.

a(n) = A151830(n) - 4 * A006763(n) - 6 * A006762(n) - 4 for n > 1. - Sean A. Irvine, Jul 28 2017

cp's OEIS Frontend

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).

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