A295686 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 1, a(2) = 2, a(3) = 1.

2, 1, 2, 1, 4, 7, 10, 15, 26, 43, 68, 109, 178, 289, 466, 753, 1220, 1975, 3194, 5167, 8362, 13531, 21892, 35421, 57314, 92737, 150050, 242785, 392836, 635623, 1028458, 1664079, 2692538, 4356619, 7049156, 11405773, 18454930, 29860705, 48315634, 78176337

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) = 1, a(2) = 2, a(3) = 1.

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A076198 A032021 A306703 * A246996 A260612 A159829

Adjacent sequences: A295683 A295684 A295685 * A295687 A295688 A295689

Keyword

nonn,easy

Author

Clark Kimberling, Nov 29 2017

Status

approved