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

Author

Andrew Howroyd, May 20 2022

Keywords

• nonn

Comments

Permuting the symbols does not change the structure.

Examples

			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.
		

Links

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

Crossrefs

Row sums of A351645.

Cf. A351638.

Programs

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) ))}