A295722 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -1, a(2) = 2, a(3) = 3.

-1, -1, 2, 3, 13, 20, 49, 77, 158, 251, 473, 756, 1357, 2177, 3790, 6095, 10397, 16748, 28169, 45429, 75646, 122099, 201841, 325988, 536021, 866105, 1418510, 2292807, 3744085, 6053276, 9862897, 15948941, 25942910, 41957387, 68162441, 110250900, 178937629

Offset: 0

Author

Clark Kimberling, Nov 29 2017

Keywords

• easy
• sign

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, 3, -2, -2)

Crossrefs

Cf. A001622, A000045, A005672.

Programs

Mathematica

LinearRecurrence[{1, 3, -2, -2}, {-1, -1, 2, 3}, 100]

Formula

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

G.f.: (-1 + 6 x^2 + 2 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).