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
Keywords
Links
- 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.
Crossrefs
Cf. A001181.
Programs
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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)))