A295681 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0, a(1) = 1, a(2) = 0, a(3) = 2.

0, 1, 0, 2, 3, 4, 6, 11, 18, 28, 45, 74, 120, 193, 312, 506, 819, 1324, 2142, 3467, 5610, 9076, 14685, 23762, 38448, 62209, 100656, 162866, 263523, 426388, 689910, 1116299, 1806210, 2922508, 4728717, 7651226, 12379944, 20031169, 32411112, 52442282, 84853395

Offset: 0

Author

Clark Kimberling, Nov 27 2017

Keywords

• nonn
• easy

Comments

Lim_{n->inf} 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)

Crossrefs

Cf. A001622, A000045.

Programs

Mathematica

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

Formula

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

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