A368636 Number of modified ascent sequences of length n avoiding the pattern 221.

1, 1, 2, 5, 14, 44, 155, 607, 2617, 12306, 62587, 341790, 1991916, 12324031, 80587935, 554826429, 4008364544, 30299290911, 239019427636, 1963239741712, 16755637216417, 148317595764043, 1359380603278377, 12880841117125364, 126007744452786277, 1270998629233371388

Offset: 0

Author

Giulio Cerbai, Jan 19 2024

Keywords

• nonn

Examples

			The shortest modified ascent sequence that contains 221 is 1221.
		

Links

• Giulio Cerbai, Pattern-avoiding modified ascent sequences, arXiv:2401.10027 [math.CO], 2024.

Crossrefs

Cf. A022493 (all modified ascents).

Programs

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 *)

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.