A295676 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 3, a(3) = -3.

1, 1, 3, -3, -1, 3, 3, -1, 1, 7, 9, 9, 17, 33, 51, 77, 127, 211, 339, 543, 881, 1431, 2313, 3737, 6049, 9793, 15843, 25629, 41471, 67107, 108579, 175679, 284257, 459943, 744201, 1204137, 1948337, 3152481, 5100819, 8253293, 13354111, 21607411, 34961523

Offset

0,3

Comments

Lim_{n->inf} 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, 0, 1, 1)

Formula

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

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A101988 A200606 A293862 * A088420 A103585 A154595

Adjacent sequences: A295673 A295674 A295675 * A295677 A295678 A295679

Keyword

easy,sign

Author

Clark Kimberling, Nov 27 2017

Status

approved