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

0,3

Links

Table of n, a(n) for n=0..35.

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).

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)

Mathematica

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

Crossrefs

Cf. A000079, A005009.

Sequence in context: A251744 A251751 A251765 * A113405 A119340 A119341

Adjacent sequences: A365059 A365060 A365061 * A365063 A365064 A365065

Keyword

nonn,easy

Author

Michael De Vlieger, Aug 23 2023

Status

approved