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%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