A365062 Enumeration of | Sort_n(123,321) |.
1, 1, 2, 4, 7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 57344, 114688, 229376, 458752, 917504, 1835008, 3670016, 7340032, 14680064, 29360128, 58720256, 117440512, 234881024, 469762048, 939524096, 1879048192, 3758096384, 7516192768, 15032385536
Offset: 0
Links
- Christopher Bao, Yunseo Choi, Katelyn Gan, and Owen Zhang, On a Conjecture by Baril, Cerbai, Khalil, and Vajnovszki on Two Restricted Stacks, arXiv:2308.09344 [math.CO], 2023. See Theorems 1.1 and 1.2, pp. 2-3.
- Index entries for linear recurrences with constant coefficients, signature (2).
Programs
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Mathematica
{1}~Join~Array[If[# <= 3, 2^(# - 1), 7*2^(# - 4)] &, 30]
Formula
a(0) = 1, a(n) = 2^(n-1) for n = 1..3, a(n) = 7*2^(n-4) for n > 3.
From Chai Wah Wu, Aug 24 2023: (Start)
a(n) = 2*a(n-1) for n > 4.
G.f.: (x^4 + x - 1)/(2*x - 1). (End)