A373343 -id:A373343 - cp's OEIS frontend

A373344 Antidiagonal sums of A373343.

1, 2, 4, 33, 394025, 201957164678370265209, 84193682293466007059985338904628711064119559738613309218248322664618484704217611109073

Offset: 1

Stefano Spezia, Jun 01 2024

nonn

The next term is too large to be included in Data.

Cf. A373343.

A373343[n_,k_]:=(n!)^(n^(k-1))/n^k; a[n_]:=Sum[A373343[n-k+1,k],{k,n}]; Array[a,7]

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.

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Jun 01 2024

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

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

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.

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

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

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

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

cp's OEIS Frontend

A373344 Antidiagonal sums of A373343.

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