A340410 Number of sets of nonempty words with a total of n letters over ternary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

1, 1, 3, 13, 36, 122, 433, 1356, 4449, 15279, 48567, 158837, 532415, 1704777, 5547148, 18335536, 58815602, 190574866, 623885902, 2000945191, 6459510350, 20998728429, 67275468661, 216477522426, 699952967976, 2239210854373, 7184690267832, 23131348476391

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: Product_{j>=1} (1+x^j)^A092255(j).

Example

a(3) = 13: {aaa}, {aab}, {aba}, {baa}, {abc}, {acb}, {bac}, {bca}, {cab}, {cba}, {aa,a}, {ab,a}, {ba,a}.

Maple

b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
      add(b(n-j, j, t-1)/j!, j=i..n/t))
    end:
g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
    end:
a:= n-> h(n$2, min(n, 3)):
seq(a(n), n=0..32);

Crossrefs

Column k=3 of A292795.

Cf. A092255.

Sequence in context: A146424 A146049 A061483 * A128288 A113115 A107136

Adjacent sequences: A340407 A340408 A340409 * A340411 A340412 A340413

Keyword

nonn

Author

Alois P. Heinz, Jan 06 2021

Status

approved