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A369322
a(n) is the number of weak ascent sequences (of any length) with n weak ascents.
2
1, 1, 3, 20, 285, 8498, 521549, 65149296, 16446593964, 8354292354562, 8517018874559019, 17400156347544892896, 71175200852044807325678, 582639858848549658827324726, 9542182685892187892079287210803, 312611431819035281373960038697247872
OFFSET
0,3
COMMENTS
Column sums of A369321.
A weak ascent sequence is a sequence [d(1), d(2), ..., d(n)] where d(1)=0, d(k)>=0, and d(k) <= 1 + asc([d(1), d(2), ..., d(k-1)]) and asc(.) counts the weak ascents d(j) >= d(j-1) of its argument.
LINKS
Beata Benyi, Anders Claesson, Mark Dukes, Weak ascent sequences and related combinatorial structures, arXiv:2111.03159 [math.CO], (4-November-2021).
MAPLE
b:= proc(n, i, t, k) option remember;
`if`(k<0, 0, `if`(n=0, `if`(k=0, 1, 0), add((d->
b(n-1, j, t+d, k-d))(`if`(j>=i, 1, 0)), j=0..t+1)))
end:
a:= n-> add(b(j, -1$2, n), j=n..n*(n+1)/2):
seq(a(n), n=0..15); # Alois P. Heinz, Jan 25 2024
CROSSREFS
Sequence in context: A136551 A266812 A086229 * A130531 A240777 A163138
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jan 20 2024
STATUS
approved