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
Alois P. Heinz, Table of n, a(n) for n = 0..50
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
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jan 20 2024
STATUS
approved