A291057 Cardinality of the smallest nonempty class of length minimal languages with exactly n nonempty words each over a countably infinite alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

1, 1, 2, 1, 4, 6, 4, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 26, 325, 2600, 14950, 65780, 230230, 657800, 1562275, 3124550, 5311735, 7726160, 9657700, 10400600, 9657700, 7726160, 5311735, 3124550, 1562275, 657800, 230230, 65780, 14950, 2600, 325, 26, 1

Offset

0,3

Comments

a(n) is the smallest nonzero term in column n of A293815.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1115

Example

a(0) = 1: {{}}.
a(1) = 1: {{a}}.
a(2) = 2: {{a,aa}, {a,ab}}.
a(3) = 1: {{a,aa,ab}}.
a(4) = 4: {{a,aa,ab,aaa}, {a,aa,ab,aab}, {a,aa,ab,aba}, {a,aa,ab,abc}}.
a(5) = 6: {{a,aa,ab,aaa,aab}, {a,aa,ab,aaa,aba}, {a,aa,ab,aaa,abc}, {a,aa,aab,aba}, {a,aa,ab,aab,ab,abc}, {a,aa,ab,aba,abc}}.
a(6) = 4: {{a,aa,ab,aaa,aab,aba}, {a,aa,ab,aaa,aab,abc}, {a,aa,ab,aaa,aba,abc}, {a,aa,ab,aab,aba,abc}}.
a(7) = 1: {{a,aa,ab,aaa,aab,aba,abc}}.
Breaking the sequence into lines after each 1 gives an irregular triangle whose j-th row equals the A000085(j)-th row of A007318 without its leftmost term. The leftmost column of this triangle is A000085:
   1;
   1;
   2,   1;
   4,   6,    4,     1;
  10,  45,  120,   210,   252,    210,    120,      45,      10,   1;
  26, 325, 2600, 14950, 65780, 230230, 657800, 1562275, 3124550, ...
  ...

Crossrefs

Cf. A000085, A007318, A293815, A294129.

Sequence in context: A375305 A343964 A345135 * A143897 A217298 A217299

Adjacent sequences: A291054 A291055 A291056 * A291058 A291059 A291060

Keyword

nonn,look

Author

Alois P. Heinz, Oct 20 2017

Status

approved