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

Author

Alois P. Heinz, Oct 23 2017

Keywords

• nonn

Comments

Numbers n such that A291057(n) equals 1.

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

Examples

			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}.
		

Links

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

Crossrefs

Cf. A000085, A245176, A291057, A293815.

Programs

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);

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.