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Triangle read by rows: cumulative sums of the rows of A049430.
2

%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