A295684 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 0, a(2) = 1, a(3) = 1.

2, 0, 1, 1, 3, 4, 6, 10, 17, 27, 43, 70, 114, 184, 297, 481, 779, 1260, 2038, 3298, 5337, 8635, 13971, 22606, 36578, 59184, 95761, 154945, 250707, 405652, 656358, 1062010, 1718369, 2780379, 4498747, 7279126, 11777874, 19057000, 30834873, 49891873, 80726747

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) = 1, a(3) = 1.

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A354668 A215086 A261440 * A276890 A276921 A339677

Adjacent sequences: A295681 A295682 A295683 * A295685 A295686 A295687

Keyword

nonn,easy

Author

Clark Kimberling, Nov 29 2017

Status

approved