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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.
3
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 23 2017
STATUS
approved