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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). 12
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

According to Barequet-Barequet-Rote, p. 260, the value DX(7, 6) = 134209 given by W. F. Lunnon is incorrect; it should be 153664, see A127670; this also affects A195762 which is the right-hand diagonal of this sequence. - Alexander Knapp, May 13 2013

LINKS

Table of n, a(n) for n=1..28.

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 7

-------------------

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 134209

...

CROSSREFS

Columns give A006762, A006763, A006764, A195762. 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,more

AUTHOR

N. J. A. Sloane, Sep 23 2011

STATUS

approved

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)