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%I #19 Sep 09 2023 18:02:19
%S 1,0,1,0,1,2,0,1,5,7,0,1,12,23,26,0,1,35,112,147,153,0,1,108,607,1019,
%T 1123,1134,0,1,369,3811,8699,10708,11027,11050,0,1,1285,25413,82535,
%U 119120,127989,128940,128987,0,1,4655,178083,846042,1493722,1725296
%N Triangle read by rows: cumulative sums of the rows of A049430.
%C T(n,k) is also the number of n-celled polyominoes made up of k-dimensional cubes, counted up to rotation, reflection, and translation.
%H Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/204187/53884">Counting hypercube Tetris pieces</a>
%F T(n,k) = Sum_{i=0..k} A049430(n,i).
%e Table begins:
%e n/k| 0 1 2 3 4 5 6 7 8
%e ---+-------------------------------------------------
%e 1| 1
%e 2| 0 1
%e 3| 0 1 2
%e 4| 0 1 5 7
%e 5| 0 1 12 23 26
%e 6| 0 1 35 112 147 153
%e 7| 0 1 108 607 1019 1123 1134
%e 8| 0 1 369 3811 8699 10708 11027 11050
%e 9| 0 1 1285 25413 82535 119120 127989 128940 128987
%Y Cf. A049429, A049430.
%Y Columns 2-4: A000105, A038119, A068870.
%Y Main diagonal is A005519.
%K nonn,hard,tabl
%O 1,6
%A _Peter Kagey_, Apr 30 2020
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