A347546 Number of involutions of doubly alternating Baxter permutations of length n.

1, 1, 1, 1, 2, 2, 3, 5, 8, 12, 16, 32, 44, 84, 105, 231, 292, 636, 768, 1792, 2166, 5080, 6012, 14592, 17234, 42198, 49336, 123088, 143536, 361190, 418971, 1066497, 1234242, 3164870, 3651296, 9436968, 10866726, 28255468, 32469716, 84925632, 97443786, 256131058

Offset

0,5

Links

Table of n, a(n) for n=0..41.

Marilena Barnabei, Flavio Bonetti, Niccolò Castronuovo, and Matteo Silimbani, Pattern avoiding alternating involutions, arXiv:2206.13877 [math.CO], 2022.

Sook Min, The Enumeration of Involutions of Doubly Alternating Baxter Permutations, Journal of the Chungcheong Mathematical Society, 34(3) (2021), 253-257.

Prog

(Python)
def b(n):
    if (0<=n<=3):
        return 1
    if (n==4):
        return 2
    if (n%2==1):
      t=0
      for k in range(1, ((n+1)//2)):
          t+=b(2*k-2)*b(n-2*k)
      return t
    else:
        s=0
        for j in range(round(n/4), (n//2)):
            s+=b(4*j-n)*b(n-2*j-1)
        return b(n-1)+s
for i in range(30):
    print(str(i)+': '+str(b(i)))

Crossrefs

Cf. A001181.

Sequence in context: A179523 A087729 A039890 * A152948 A018136 A243853

Adjacent sequences: A347543 A347544 A347545 * A347547 A347548 A347549

Keyword

nonn

Author

Sook Min, Sep 06 2021

Status

approved