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A369325
a(n) is the number of words of length n over the alphabet [n], avoiding 120 and 210, and sortable by a stack of depth 2.
2
0, 1, 4, 25, 176, 1281, 9472, 70785, 533248, 4042753, 30808064, 235778049, 1810915328, 13951401985, 107765334016, 834322202625, 6472333459456, 50299072937985, 391513776848896, 3051764505903105, 23818327111499776, 186112536460918785, 1455790849571946496, 11398349517712523265
OFFSET
0,3
LINKS
Toufik Mansour, Howard Skogman, and Rebecca Smith, Sorting inversion sequences, arXiv:2401.06662 [math.CO], 2024. See Theorem 3.18 at page 10.
FORMULA
a(n) = A000035(n) + 2^n*Sum_{i=0..floor((n-2)/2)} binomial(2*(n - i)- 3, n - 1).
a(n) ~ 8^(n-1)*hypergeom([1, 1 - n/2, (3 - n)/2], [(3 - 2*n)/2, 2 - n], 1)/sqrt(n*Pi).
MATHEMATICA
a[n_] := (1-(-1)^n)/2 + 2^n*Sum[Binomial[2(n-i)-3, n-1], {i, 0, Floor[(n-2)/2]}]; Array[a, 24, 0]
CROSSREFS
Main diagonal of A369324.
Sequence in context: A093683 A006348 A213608 * A324169 A213231 A051820
KEYWORD
nonn
AUTHOR
Stefano Spezia, Jan 20 2024
STATUS
approved