A286062 a(n) = 2*a(n-1) + a(n-2) - a(n-3), where a(0) = 2, a(1) = 3, a(2) = 6.

2, 3, 6, 13, 29, 65, 146, 328, 737, 1656, 3721, 8361, 18787, 42214, 94854, 213135, 478910, 1076101, 2417977, 5433145, 12208166, 27431500, 61638021, 138499376, 311205273, 699271901, 1571249699, 3530566026, 7933109850, 17825536027, 40053615878, 89999657933

Offset

0,1

Comments

Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->001, 1->011, starting with 00; see A286939.

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (2, 1, -1).

Formula

a(n) = 2*a(n-1) + a(n-2) - a(n-3), where a(0) = 2, a(1) = 3, a(2) = 6.

G.f.: (2 - x - 2*x^2)/(1 - 2*x - x^2 + x^3).

Mathematica

LinearRecurrence[{2, 1, -1}, {2, 3, 6}, 40]

Crossrefs

Cf. A286059.

Sequence in context: A197463 A032048 A287128 * A219226 A238426 A032066

Adjacent sequences: A286059 A286060 A286061 * A286063 A286064 A286065

Keyword

nonn,easy

Author

Clark Kimberling, Jun 05 2017

Status

approved