A128249 T(n,k) is the number of unlabeled acyclic single-source automata with n transient states on a (k+1)-letter input alphabet.

1, 3, 1, 16, 7, 1, 127, 139, 15, 1, 1363, 5711, 1000, 31, 1, 18628, 408354, 189035, 6631, 63, 1, 311250, 45605881, 79278446, 5470431, 42196, 127, 1, 6173791, 7390305396, 63263422646, 12703473581, 147606627, 262459, 255, 1, 142190703, 1647470410551

Offset

1,2

Comments

Table with rows n=1,2,... and columns k=1,2,3,... is read along antidiagonals.

Links

Table of n, a(n) for n=1..38.

David Callan, A determinant of Stirling Cycle Numbers Count Unlabeled Acyclic Single-Source Automata math.CO/0704.0004.

Manosij Ghosh Dastidar and Michael Wallner, Asymptotics of relaxed k-ary trees, arXiv:2404.08415 [math.CO], 2024. See p. 1.4.

Maple

T := proc(n, k) local kn, A, i, j ; kn := k*n ; A := matrix(kn, kn) ; for i from 1 to kn do for j from 1 to kn do A[i, j] := abs(combinat[stirling1](floor((i-1)/k)+2, floor((i-1)/k)+1+i-j)) ; od ; od ; linalg[det](A) ; end: for d from 1 to 9 do for n from d to 1 by -1 do k := d+1-n ; printf("%d, ", T(n, k)) ; od ; od;

Mathematica

t[n_, k_] := Module[{kn, a, i, j}, kn = k*n; For[i = 1, i <= kn, i++, For[j = 1, j <= kn, j++, a[i, j] = Abs[StirlingS1[Floor[(i-1)/k]+2, Max[0, Floor[(i-1)/k]+1+i-j]]]]]; Det[Array[a, {kn, kn}]]]; Table[t[n-k, k], {n, 1, 10}, {k, 1, n-1}] // Flatten (* Jean-François Alcover, Jan 10 2014, translated from Maple *)

Crossrefs

Cf. A082162, A082161.

Sequence in context: A143565 A143018 A102012 * A071211 A222029 A038675

Adjacent sequences: A128246 A128247 A128248 * A128250 A128251 A128252

Keyword

nonn,tabl,changed

Author

R. J. Mathar, May 09 2007

Status

approved