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A368636
Number of modified ascent sequences of length n avoiding the pattern 221.
0
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
0,3
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
Cf. A022493 (all modified ascents).
Sequence in context: A350492 A014322 A095148 * A060996 A134378 A101226
KEYWORD
nonn
AUTHOR
Giulio Cerbai, Jan 19 2024
STATUS
approved