A385583 Triangle read by rows: T(n,d) is the number of free d-dimensional polysticks of size n.

1, 1, 2, 1, 5, 7, 1, 16, 28, 31, 1, 55, 160, 199, 205, 1, 222, 1085, 1651, 1768, 1779

Offset

1,3

Comments

If d > n, there are T(n,n) such polysticks. The triangle only includes the values for d <= n.

Links

Table of n, a(n) for n=1..21.

Index entries for sequences related to polyominoes.

Formula

T(n,d) = Sum_{k=1..d} A365566(n,k).

Example

Triangle begins:
  n\d| 1   2    3    4    5    6
  ---+--------------------------
  1  | 1
  2  | 1   2
  3  | 1   5    7
  4  | 1  16   28   31
  5  | 1  55  160  199  205
  6  | 1 222 1085 1651 1768 1779

Crossrefs

Cf. A330891 (polyominoes), A365565 (main diagonal), A365566, A385581 (fixed).

Columns: A019988 (d=2), A365559 (d=3), A365561 (d=4), A365563 (d=5).

Sequence in context: A144505 A369527 A370382 * A059039 A392058 A332022

Adjacent sequences: A385580 A385581 A385582 * A385584 A385585 A385586

Keyword

nonn,tabl,more

Author

Pontus von Brömssen, Jul 04 2025

Status

approved