A288925 a(n) = a(n-1) + a(n-2) + 3*a(n-4) - 2*a(n-5) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 13, a(4) = 26.

2, 4, 8, 13, 26, 47, 89, 159, 300, 548, 1021, 1868, 3471, 6383, 11821, 21766, 40264, 74237, 137198, 253091, 467549, 862823, 1593492, 2941192, 5431149, 10025712, 18511691, 34173995, 63096749, 116485582, 215065980, 397050165, 733058402, 1353371815, 2498656993

Offset

0,1

Comments

Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->1000, 10->0001, starting with 00; see A288226.

Links

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

Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 3, -2).

Formula

a(n) = a(n-1) + a(n-2) + 3*a(n-4) - 2*a(n-5) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 13, a(4) = 26.

G.f.: (1 + x)*(2 + 2*x^2 - x^3) / (1 - x - x^2 - 3*x^4 + 2*x^5). - Colin Barker, Jun 25 2017

Mathematica

LinearRecurrence[{1, 1, 0, 3, -2}, {2, 4, 8, 13, 26}, 40]

Prog

(PARI) Vec((1 + x)*(2 + 2*x^2 - x^3) / (1 - x - x^2 - 3*x^4 + 2*x^5) + O(x^50)) \\ Colin Barker, Jun 25 2017

Crossrefs

Cf. A289026.

Sequence in context: A094767 A263292 A026643 * A018285 A026665 A369704

Adjacent sequences: A288922 A288923 A288924 * A288926 A288927 A288928

Keyword

nonn,easy

Author

Clark Kimberling, Jun 25 2017

Status

approved