A294129 Numbers n for which exactly one length minimal language exists having exactly n nonempty words 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.

0, 1, 3, 7, 17, 43, 119, 351, 1115, 3735, 13231, 48927, 189079, 757583, 3148063, 13497599, 59704335, 271503647, 1268817471, 6078518911, 29837183007, 149789875903, 768674514815, 4026518397439, 21518708975039, 117199152735615, 650184360936191, 3670861106911743

Offset

1,3

Comments

Numbers n such that A291057(n) equals 1.

Numbers n such that the smallest nonzero term in column n of A293815 equals 1.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..800

Formula

a(n) = a(n-1) + A000085(n-1) for n>1, a(1) = 0.

a(n) = 2*a(n-1)+(n-3)*a(n-2)-(n-2)*a(n-3) for n>= 4, a(n) = n*(n-1)/2 for n<4.

a(n) = A245176(n-1) - 1 for n>0.

Example

0 is a term because there is only one length minimal language with 0 words: {}.
1 is a term: {a}.
3 is a term: {a, aa, ab}.
7 is a term: {a, aa, ab, aaa, aab, aba, abc}.
17 is a term: {a, aa, ab, aaa, aab, aba, abc, aaaa, aaab, aaba, aabb, aabc, abaa, abab, abac, abca, abcd}.

Maple

a:= proc(n) option remember; `if`(n<4, n*(n-1)/2,
      2*a(n-1)+(n-3)*a(n-2)-(n-2)*a(n-3))
    end:
seq(a(n), n=1..30);

Crossrefs

Cf. A000085, A245176, A291057, A293815.

Sequence in context: A153133 A123601 A115325 * A308589 A018025 A018026

Adjacent sequences: A294126 A294127 A294128 * A294130 A294131 A294132

Keyword

nonn

Author

Alois P. Heinz, Oct 23 2017

Status

approved