A373343 Array read by ascending antidiagonals: A(n,k) is the number of cyclic de Bruijn sequences of order k and alphabet of size n, with k > 0.

1, 1, 1, 2, 1, 1, 6, 24, 2, 1, 24, 20736, 373248, 16, 1, 120, 995328000, 189321481108517289984, 12635683568857645056, 2048, 1

Offset

1,4

Comments

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

Links

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

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.

Formula

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

A(n,k) = A373341(n,k)/A003992(n,k).

Example

The array begins:
  1,  1,      1,                    1, ...
  1,  1,      2,                   16, ...
  2, 24, 373248, 12635683568857645056, ...
  ...

Mathematica

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

Crossrefs

Cf. A000012 (n=1), A000142 (k=1), A003992, A016031 (n=2), A373341 (acyclic), A373344 (antidiagonal sums).

Sequence in context: A214631 A025270 A249450 * A331501 A247450 A178234

Adjacent sequences: A373340 A373341 A373342 * A373344 A373345 A373346

Keyword

nonn,tabl

Author

Stefano Spezia, Jun 01 2024

Status

approved