A288523 a(n) = a(n-1) + a(n-2) + a(n-3) - 2*a(n-4) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 5, a(3) = 8, a(4) = 11.

2, 4, 5, 8, 11, 16, 25, 36, 55, 84, 125, 192, 291, 440, 673, 1020, 1551, 2364, 3589, 5464, 8315, 12640, 19241, 29268, 44519, 67748, 103053, 156784, 238547, 362888, 552113, 839980, 1277887, 1944204, 2957845, 4499976, 6846251, 10415664, 15846201, 24108164

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->0101, 10->010, starting with 00; see A288520.

Links

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

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

Formula

a(n) = a(n-1) + a(n-2) + a(n-3) - 2*a(n-4) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 5, a(3) = 8, a(4) = 11.

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

Mathematica

Join[{2}, LinearRecurrence[{1, 1, 1, -2}, {4, 5, 8, 11}, 40]]

Crossrefs

Cf. A288520.

Sequence in context: A039867 A237754 A182564 * A240179 A295032 A280017

Adjacent sequences: A288520 A288521 A288522 * A288524 A288525 A288526

Keyword

nonn,easy

Author

Clark Kimberling, Jun 13 2017

Status

approved