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

1,6

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.

Links

Table of n, a(n) for n=1..52.

Code Golf Stack Exchange, Counting hypercube Tetris pieces

Formula

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

Example

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

Crossrefs

Cf. A049429, A049430.

Columns 2-4: A000105, A038119, A068870.

Main diagonal is A005519.

Sequence in context: A010028 A151860 A338774 * A089627 A306534 A344392

Adjacent sequences: A330888 A330889 A330890 * A330892 A330893 A330894

Keyword

nonn,hard,tabl

Author

Peter Kagey, Apr 30 2020

Status

approved