A369327 a(n) is the number of words of length n over the alphabet [n] and sortable by a (2,1)-pop stack of depth 2.

1, 1, 4, 24, 149, 923, 5784, 36708, 235156, 1516864, 9838018, 64093998, 419137378, 2749637566, 18087479624, 119263349200, 788015054253, 5216212564723, 34584497597602, 229635524379026, 1526740206967913, 10162620233598959, 67719554546286284, 451699650863065424

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Toufik Mansour, Howard Skogman, and Rebecca Smith, Sorting inversion sequences, arXiv:2401.06662 [math.CO], 2024. See Theorem 3.25 at page 13.

Formula

a(n) = A369326(n, n).

Mathematica

A369326[n_, k_]:=SeriesCoefficient[((1-x)(1-2x)-((1-x)(1-2x)+x^2)y)/((1-x)(1-2x)-(1-x)(2-3x)y+(1-2x)y^2), {x, 0, n}, {y, 0, k}]; a[n_]:=A369326[n, n]; Array[a, 24, 0]

Crossrefs

Main diagonal of A369326.

Cf. A369325.

Sequence in context: A225050 A045738 A215708 * A192806 A347915 A262407

Adjacent sequences: A369324 A369325 A369326 * A369328 A369329 A369330

Keyword

nonn

Author

Stefano Spezia, Jan 20 2024

Status

approved