OFFSET
0,3
LINKS
Giulio Cerbai, Pattern-avoiding modified ascent sequences, arXiv:2401.10027 [math.CO], 2024.
FORMULA
a(n) = Sum_{k=1..n} Sum_{i=1..k} S2(k-1,i-1) * binomial(n-1-k+i,i-1) for n >= 1, a(0)=1, where S2(n,i) are the Stirling numbers of the second kind.
EXAMPLE
The shortest modified ascent sequence that contains 221 is 1221.
MATHEMATICA
a[0]=1; a[n_]:=Sum[Sum[StirlingS2[k-1, i-1] Binomial[n-1-k+i, i-1], {i, k}], {k, n}]; Array[a, 26, 0] (* Stefano Spezia, Jan 20 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Giulio Cerbai, Jan 19 2024
STATUS
approved