A295859 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = 0, a(2) = 1, a(3) = 1.

-2, 0, 1, 1, 8, 9, 29, 38, 91, 129, 268, 397, 761, 1158, 2111, 3269, 5764, 9033, 15565, 24598, 41699, 66297, 111068, 177365, 294577, 471942, 778807, 1250749, 2054132, 3304881, 5408165, 8713046, 14219515, 22932561, 37348684, 60281245, 98023145, 158304390

Offset: 0

Author

Clark Kimberling, Jan 07 2018

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, A295860.

Programs

Mathematica

LinearRecurrence[{1, 3, -2, -2}, {-2, 0, 1, 1}, 100]

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 + 7 x^2 - 4 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).