A295861 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = -1, a(2) = 0, a(3) = 1.

-2, -1, 0, 1, 7, 12, 31, 51, 106, 173, 327, 532, 955, 1551, 2698, 4377, 7459, 12092, 20319, 32923, 54778, 88725, 146575, 237348, 390067, 631511, 1033866, 1673569, 2732011, 4421964, 7203127, 11657859, 18959290, 30682685, 49838583, 80652340, 130884139

Offset

0,1

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)

Formula

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

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

Mathematica

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

Crossrefs

Cf. A001622, A000045, A295859, A295860.

Sequence in context: A331161 A176887 A076422 * A337272 A373571 A058998

Adjacent sequences: A295858 A295859 A295860 * A295862 A295863 A295864

Keyword

easy,sign

Author

Clark Kimberling, Jan 07 2018

Status

approved