A295735 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 0, a(3) = 1.

0, -1, 0, 1, 3, 8, 15, 31, 54, 101, 171, 304, 507, 875, 1446, 2449, 4023, 6728, 11007, 18247, 29766, 49037, 79827, 130912, 212787, 347795, 564678, 920665, 1493535, 2430584, 3940503, 6403855, 10377126, 16846517, 27289179, 44266768, 71687019, 116215931

Offset

0,5

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

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

Mathematica

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

Crossrefs

Cf. A001622, A000045, A005672.

Sequence in context: A135350 A068038 A196087 * A309052 A328858 A277224

Adjacent sequences: A295732 A295733 A295734 * A295736 A295737 A295738

Keyword

easy,sign

Author

Clark Kimberling, Nov 30 2017

Status

approved