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A347546 Number of involutions of doubly alternating Baxter permutations of length n. 0

%I #20 Jun 29 2022 02:50:48

%S 1,1,1,1,2,2,3,5,8,12,16,32,44,84,105,231,292,636,768,1792,2166,5080,

%T 6012,14592,17234,42198,49336,123088,143536,361190,418971,1066497,

%U 1234242,3164870,3651296,9436968,10866726,28255468,32469716,84925632,97443786,256131058

%N Number of involutions of doubly alternating Baxter permutations of length n.

%H Marilena Barnabei, Flavio Bonetti, Niccolò Castronuovo, and Matteo Silimbani, <a href="https://arxiv.org/abs/2206.13877">Pattern avoiding alternating involutions</a>, arXiv:2206.13877 [math.CO], 2022.

%H Sook Min, <a href="https://doi.org/10.14403/jcms.2021.34.3.253">The Enumeration of Involutions of Doubly Alternating Baxter Permutations</a>, Journal of the Chungcheong Mathematical Society, 34(3) (2021), 253-257.

%o (Python)

%o def b(n):

%o if (0<=n<=3):

%o return 1

%o if (n==4):

%o return 2

%o if (n%2==1):

%o t=0

%o for k in range(1, ((n+1)//2)):

%o t+=b(2*k-2)*b(n-2*k)

%o return t

%o else:

%o s=0

%o for j in range(round(n/4), (n//2)):

%o s+=b(4*j-n)*b(n-2*j-1)

%o return b(n-1)+s

%o for i in range(30):

%o print(str(i)+': '+str(b(i)))

%Y Cf. A001181.

%K nonn

%O 0,5

%A _Sook Min_, Sep 06 2021

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Last modified June 20 17:22 EDT 2024. Contains 373530 sequences. (Running on oeis4.)