A288668 a(n) = a(n-2) + 2*a(n-3) for n >= 3, where a(0) = 2, a(2) = 4, a(3) = 5.

2, 4, 5, 8, 13, 18, 29, 44, 65, 102, 153, 232, 357, 538, 821, 1252, 1897, 2894, 4401, 6688, 10189, 15490, 23565, 35868, 54545, 82998, 126281, 192088, 292277, 444650, 676453, 1029204, 1565753, 2382110, 3624161, 5513616, 8388381, 12761938, 19415613, 29538700

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->0110, 10->000, starting with 00; see A288665.

Links

Clark Kimberling, Table of n, a(n) for n = 0..10000

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

Formula

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

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

Mathematica

LinearRecurrence[{0, 1, 2}, {2, 4, 5}, 40]

Crossrefs

Cf. A288665.

Sequence in context: A164571 A238589 A327045 * A264800 A293189 A278695

Adjacent sequences: A288665 A288666 A288667 * A288669 A288670 A288671

Keyword

nonn,easy

Author

Clark Kimberling, Jun 15 2017

Status

approved