A295736 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -2, a(2) = -2, a(3) = 1.

1, -2, -2, 1, -3, 8, 1, 29, 22, 91, 97, 268, 333, 761, 1030, 2111, 3013, 5764, 8521, 15565, 23574, 41699, 64249, 111068, 173269, 294577, 463750, 778807, 1234365, 2054132, 3272113, 5408165, 8647510, 14219515, 22801489, 37348684, 60019101, 98023145, 157780102

Offset: 0

Author

Clark Kimberling, Nov 30 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, -2, -2, 1}, 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) = 1.

G.f.: (1 - 3 x - 3 x^2 + 11 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).