A049430 - OEIS

%I #42 Aug 24 2023 12:05:49

%S 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,

%T 11,0,1,368,3442,4888,2009,319,23,0,1,1284,24128,57122,36585,8869,951,

%U 47,0,1,4654,173428,667959,647680,231574,36988,2862,106,0,1,17072,1262464,7799183,11173880,5712765,1297366,146578,8516,235

%N 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).

%H W. F. Lunnon, <a href="http://dx.doi.org/10.1093/comjnl/18.4.366">Counting multidimensional polyominoes</a>. Computer Journal 18 (1975), no. 4, pp. 366-367.

%e Triangle begins:

%e 1

%e 0 1

%e 0 1     1

%e 0 1     4       2

%e 0 1    11      11       3

%e 0 1    34      77      35        6

%e 0 1   107     499     412      104      11

%e 0 1   368    3442    4888     2009     319      23

%e 0 1  1284   24128   57122    36585    8869     951     47

%e 0 1  4654  173428  667959   647680  231574   36988   2862  106

%e 0 1 17072 1262464 7799183 11173880 5712765 1297366 146578 8516 235

%e ...

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

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

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

%Y Cf. A330891 (cumulative sums of the rows).

%K nonn,nice,tabl,hard

%O 1,9

%A Richard C. Schroeppel

%E Edited by _N. J. A. Sloane_, Sep 23 2011

%E More terms from _John Niss Hansen_, Mar 31 2015