cp's OEIS Frontend

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.

%I A294129 #9 Oct 23 2017 12:17:32
%S A294129 0,1,3,7,17,43,119,351,1115,3735,13231,48927,189079,757583,3148063,
%T A294129 13497599,59704335,271503647,1268817471,6078518911,29837183007,
%U A294129 149789875903,768674514815,4026518397439,21518708975039,117199152735615,650184360936191,3670861106911743
%N 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.
%C A294129 Numbers n such that A291057(n) equals 1.
%C A294129 Numbers n such that the smallest nonzero term in column n of A293815 equals 1.
%H A294129 Alois P. Heinz, <a href="/A294129/b294129.txt">Table of n, a(n) for n = 1..800</a>
%F A294129 a(n) = a(n-1) + A000085(n-1) for n>1, a(1) = 0.
%F A294129 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.
%F A294129 a(n) = A245176(n-1) - 1 for n>0.
%e A294129 0 is a term because there is only one length minimal language with 0 words: {}.
%e A294129 1 is a term: {a}.
%e A294129 3 is a term: {a, aa, ab}.
%e A294129 7 is a term: {a, aa, ab, aaa, aab, aba, abc}.
%e A294129 17 is a term: {a, aa, ab, aaa, aab, aba, abc, aaaa, aaab, aaba, aabb, aabc, abaa, abab, abac, abca, abcd}.
%p A294129 a:= proc(n) option remember; `if`(n<4, n*(n-1)/2,
%p A294129       2*a(n-1)+(n-3)*a(n-2)-(n-2)*a(n-3))
%p A294129     end:
%p A294129 seq(a(n), n=1..30);
%Y A294129 Cf. A000085, A245176, A291057, A293815.
%K A294129 nonn
%O A294129 1,3
%A A294129 _Alois P. Heinz_, Oct 23 2017