A295858 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) = 0, a(3) = 1.

-2, 0, 0, 1, 5, 8, 21, 33, 70, 111, 213, 340, 617, 989, 1734, 2787, 4777, 7692, 12981, 20929, 34934, 56375, 93357, 150756, 248209, 401013, 657414, 1062523, 1736321, 2807036, 4576125, 7399545, 12041206, 19473519, 31645797, 51184852, 83092793, 134408717

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) = 0, a(2) = 0, a(3) = 1.

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A331106 A318373 A138497 * A113129 A127826 A228866

Adjacent sequences: A295855 A295856 A295857 * A295859 A295860 A295861

Keyword

easy,sign

Author

Clark Kimberling, Dec 01 2017

Status

approved