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A347546 Number of involutions of doubly alternating Baxter permutations of length n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
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.
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
KEYWORD
nonn
AUTHOR
Sook Min, Sep 06 2021
STATUS
approved

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Last modified May 19 07:05 EDT 2024. Contains 372666 sequences. (Running on oeis4.)