A295689 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 0, a(2) = 2, a(3) = 1

2, 0, 2, 1, 3, 5, 8, 12, 20, 33, 53, 85, 138, 224, 362, 585, 947, 1533, 2480, 4012, 6492, 10505, 16997, 27501, 44498, 72000, 116498, 188497, 304995, 493493, 798488, 1291980, 2090468, 3382449, 5472917, 8855365, 14328282, 23183648, 37511930, 60695577, 98207507

Offset

0,1

Comments

a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).

Links

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

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

Formula

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 0, a(2) = 2, a(3) = 1.

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

Mathematica

LinearRecurrence[{1, 0, 1, 1}, {2, 0, 2, 1}, 100]

Crossrefs

Cf. A001622, A000045.

Sequence in context: A197317 A035573 A361850 * A305804 A053470 A308202

Adjacent sequences: A295686 A295687 A295688 * A295690 A295691 A295692

Keyword

nonn,easy

Author

Clark Kimberling, Nov 29 2017

Status

approved