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A351642 Number of length n word structures with all distinct runs using an infinite alphabet. 4
1, 1, 2, 4, 10, 26, 74, 218, 668, 2116, 6928, 23254, 79998, 281694, 1011956, 3704900, 13815692, 52386978, 201787950, 789178950, 3130824160, 12589367840, 51287685476, 211557376938, 883067740514, 3728494418330, 15916998678040, 68672820917088, 299331260431104 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Permuting the symbols will not change the structure.
Equivalently, a(n) is the number of restricted growth strings [s(0), s(1), ..., s(n-1)] where s(0)=0 and s(i) <= 1 + max(prefix) for i >= 1 and all runs are distinct.
LINKS
EXAMPLE
The a(4) = 10 words are 1111, 1112, 1121, 1122, 1211, 1222, 1123, 1223, 1233, 1234.
PROG
(PARI) \\ See A351641 for R, S.
seq(n)={my(q=S(n)); concat([1], sum(k=1, n, R(q^k-1)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)/r!) )); }
CROSSREFS
Row sums of A351641.
The initial terms are similar to A206464.
Sequence in context: A279544 A245898 A230662 * A206464 A089429 A049143
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Feb 15 2022
STATUS
approved

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Last modified February 21 16:55 EST 2024. Contains 370237 sequences. (Running on oeis4.)