A295730 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = 0, a(2) = 0, a(3) = 1.

-1, 0, 0, 1, 3, 6, 13, 23, 44, 75, 135, 226, 393, 651, 1108, 1823, 3059, 5010, 8325, 13591, 22428, 36531, 59983, 97538, 159569, 259155, 422820, 686071, 1117083, 1811346, 2944813, 4772543, 7750124, 12555435, 20371095, 32992066, 53494233, 86617371, 140373748

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, 0, 0, 1}, 100]

Formula

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

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