A351732 Number of length n word structures using an infinite alphabet with all distinct run-lengths and the first run length of a symbol less than that of previous symbols.

1, 1, 1, 2, 2, 3, 7, 8, 12, 17, 46, 51, 84, 114, 172, 437, 520, 810, 1153, 1699, 2298, 6075, 6955, 11219, 15561, 23308, 31133, 45544, 107379, 128475, 200201, 281480, 413389, 561028, 806643, 1071165, 2514418, 2952086, 4619012, 6364285, 9436458

Offset

0,4

Comments

Permuting the symbols does not change the structure.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Example

The a(3) = 2 word structures are 111, 112.
The a(4) = 2 word structures are 1111, 1112.
The a(5) = 3 word structures are 11111, 11112, 11122.
The a(6) = 7 word structures are 111111, 111112, 111122, 111221, 111211, 112111, 111223.

Prog

(PARI)
P(n) = {Vec(-1 + prod(k=1, n, 1 + y*x^k + O(x*x^n)))}
R(u, k) = {k*[subst(serlaplace(p)/y, y, k-1) | p<-u]}
seq(n)={my(u=P(n)); concat([1], sum(k=1, n, R(u, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)/(r!)^2) ))}

Crossrefs

Row sums of A351645.

Cf. A351638.

Sequence in context: A259254 A095017 A141559 * A211395 A160433 A043550

Adjacent sequences: A351729 A351730 A351731 * A351733 A351734 A351735

Keyword

nonn

Author

Andrew Howroyd, May 20 2022

Status

approved