A287128 a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5), where a(0) = 2, a(1) =3, a(2) = 6, a(3)=13, a(4) = 29.

2, 3, 6, 13, 29, 65, 145, 323, 719, 1599, 3555, 7903, 17567, 39047, 86791, 192911, 428783, 953055, 2118351, 4708447, 10465439, 23261471, 51703135, 114920255, 255432575, 567748479, 1261931199, 2804887039, 6234405887, 13857177215, 30800266111, 68459569919

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->110, starting with 00; see A287125.

Links

Clark Kimberling, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (3, -2, 2, -4, 2).

Formula

a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5), where a(0) = 2, a(1) =3, a(2) = 6, a(3)=13, a(4) = 29..

G.f.: (-2 + 3*x - x^2 + 3*x^3 - 4*x^4)/(-1 + 3*x - 2*x^2 + 2*x^3 - 4*x^4 + 2*x^5).

Mathematica

LinearRecurrence[{3, -2, 2, -4, 2}, {2, 3, 6, 13, 29}, 40]

Crossrefs

Cf. A287125.

Sequence in context: A316770 A197463 A032048 * A286062 A219226 A238426

Adjacent sequences: A287125 A287126 A287127 * A287129 A287130 A287131

Keyword

nonn,easy

Author

Clark Kimberling, Jun 06 2017

Status

approved