A330891 Triangle read by rows: cumulative sums of the rows of A049430.

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, 1123, 1134, 0, 1, 369, 3811, 8699, 10708, 11027, 11050, 0, 1, 1285, 25413, 82535, 119120, 127989, 128940, 128987, 0, 1, 4655, 178083, 846042, 1493722, 1725296

Offset: 1

Author

Peter Kagey, Apr 30 2020

Keywords

• nonn
• hard
• tabl

Comments

T(n,k) is also the number of n-celled polyominoes made up of k-dimensional cubes, counted up to rotation, reflection, and translation.

Examples

			Table begins:
n/k| 0 1    2     3     4      5      6      7      8
---+-------------------------------------------------
  1| 1
  2| 0 1
  3| 0 1    2
  4| 0 1    5     7
  5| 0 1   12    23    26
  6| 0 1   35   112   147    153
  7| 0 1  108   607  1019   1123   1134
  8| 0 1  369  3811  8699  10708  11027  11050
  9| 0 1 1285 25413 82535 119120 127989 128940 128987
		

Links

• Code Golf Stack Exchange, Counting hypercube Tetris pieces

Crossrefs

Cf. A049429, A049430.

Columns 2-4: A000105, A038119, A068870.

Main diagonal is A005519.

Formula

T(n,k) = Sum_{i=0..k} A049430(n,i).