%I #41 Aug 25 2023 08:50:57

%S 1,1,2,4,7,14,28,56,112,224,448,896,1792,3584,7168,14336,28672,57344,

%T 114688,229376,458752,917504,1835008,3670016,7340032,14680064,

%U 29360128,58720256,117440512,234881024,469762048,939524096,1879048192,3758096384,7516192768,15032385536

%N Enumeration of | Sort_n(123,321) |.

%H Christopher Bao, Yunseo Choi, Katelyn Gan, and Owen Zhang, <a href="https://arxiv.org/abs/2308.09344">On a Conjecture by Baril, Cerbai, Khalil, and Vajnovszki on Two Restricted Stacks</a>, arXiv:2308.09344 [math.CO], 2023. See Theorems 1.1 and 1.2, pp. 2-3.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).

%F a(0) = 1, a(n) = 2^(n-1) for n = 1..3, a(n) = 7*2^(n-4) for n > 3.

%F From _Chai Wah Wu_, Aug 24 2023: (Start)

%F a(n) = 2*a(n-1) for n > 4.

%F G.f.: (x^4 + x - 1)/(2*x - 1). (End)

%t {1}~Join~Array[If[# <= 3, 2^(# - 1), 7*2^(# - 4)] &, 30]

%Y Cf. A000079, A005009.

%K nonn,easy

%O 0,3

%A _Michael De Vlieger_, Aug 23 2023