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
Keywords
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
Programs
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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);
Comments