A295675 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 2, a(3) = -2.

1, 1, 2, -2, 0, 3, 3, 1, 4, 10, 14, 19, 33, 57, 90, 142, 232, 379, 611, 985, 1596, 2586, 4182, 6763, 10945, 17713, 28658, 46366, 75024, 121395, 196419, 317809, 514228, 832042, 1346270, 2178307, 3524577, 5702889, 9227466, 14930350, 24157816, 39088171

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) = 2, a(3) = -2.

G.f.: (-1 - x^2 + 5 x^3)/(-1 + x + x^3 + x^4).

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A048142 A071426 A288530 * A135356 A259016 A379225

Adjacent sequences: A295672 A295673 A295674 * A295676 A295677 A295678

Keyword

easy,sign

Author

Clark Kimberling, Nov 27 2017

Status

approved