A373341 Array read by ascending antidiagonals: A(n,k) is the number of acyclic de Bruijn sequences of order k and alphabet of size n, with k > 0.

1, 2, 1, 6, 4, 1, 24, 216, 16, 1, 120, 331776, 10077696, 256, 1, 720, 24883200000, 12116574790945106558976, 1023490369077469249536, 65536, 1

Offset: 1

Author

Stefano Spezia, Jun 01 2024

Keywords

• nonn
• tabl

Comments

The 7th antidiagonal is too large to be inserted in Data.

Examples

			The array begins:
   1,      1,                       1, ...
   2,      4,                      16, ...
   6,    216,                10077696, ...
  24, 331776, 12116574790945106558976, ...
  ...
		

Links

• D. Condon, Yuxin Wang, and E. Yang, De Bruijn Polyominoes, arXiv:2405.18543 [math.CO], 2024. See page 5.
• T. van Aardenne-Ehrenfest and N. G. de Brujin, Circuits and Trees in Oriented Linear Graphs. In: Simon Stevin 28 (1951), pp. 203-217.

Crossrefs

Cf. A000012 (n=1), A000142 (k=1), A001146, A003992, A036740 (k=2), A373342 (antidiagonal sums), A373343 (cyclic).

Programs

Mathematica

A[n_,k_]:=(n!)^(n^(k-1)); Table[A[n-k+1,k],{n,6},{k,n}]//Flatten

Formula

A(n,k) = (n!)^(n^(k-1)).

A(2,n) = A001146(n-1).