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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.
2
1, 2, 1, 6, 4, 1, 24, 216, 16, 1, 120, 331776, 10077696, 256, 1, 720, 24883200000, 12116574790945106558976, 1023490369077469249536, 65536, 1
OFFSET
1,2
COMMENTS
The 7th antidiagonal is too large to be inserted in Data.
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.
FORMULA
A(n,k) = (n!)^(n^(k-1)).
A(2,n) = A001146(n-1).
EXAMPLE
The array begins:
1, 1, 1, ...
2, 4, 16, ...
6, 216, 10077696, ...
24, 331776, 12116574790945106558976, ...
...
MATHEMATICA
A[n_, k_]:=(n!)^(n^(k-1)); Table[A[n-k+1, k], {n, 6}, {k, n}]//Flatten
CROSSREFS
Cf. A000012 (n=1), A000142 (k=1), A001146, A003992, A036740 (k=2), A373342 (antidiagonal sums), A373343 (cyclic).
Sequence in context: A167560 A132159 A112356 * A135885 A162312 A141715
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Jun 01 2024
STATUS
approved