A385582 Triangle read by rows: T(n,d) is the number of fixed, properly d-dimensional polysticks of size n.

1, 1, 4, 1, 20, 32, 1, 86, 420, 400, 1, 370, 4164, 10368, 6912, 1, 1626, 38205, 186552, 301840, 153664, 1, 7310, 343380, 2934560, 8637760, 10223616, 4194304, 1, 33464, 3086049, 43517697, 207353960, 427708848, 396809280, 136048896

Offset: 1

Author

Pontus von Brömssen, Jul 04 2025

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  n\d| 1     2       3        4         5         6         7         8
  ---+-----------------------------------------------------------------
  1  | 1
  2  | 1     4
  3  | 1    20      32
  4  | 1    86     420      400
  5  | 1   370    4164    10368      6912
  6  | 1  1626   38205   186552    301840    153664
  7  | 1  7310  343380  2934560   8637760  10223616   4194304
  8  | 1 33464 3086049 43517697 207353960 427708848 396809280 136048896
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..78 (first 12 rows)
• Stephan Mertens and Cristopher Moore, Series expansion of the percolation threshold on hypercubic lattices, J. Phys. A: Math. Theor., 51 (2018), 475001; arXiv:1805.02701 [cond-mat.stat-mech], 2018.
• Index entries for sequences related to polyominoes.

Crossrefs

Cf. A127670 (main diagonal), A195739 (polyominoes), A365566 (free), A385581.

Formula

T(n,d) = Sum_{k=1..d} (-1)^(d-k)*binomial(d,k)*A385581(n,k).