A295677 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 4, a(3) = -3.

1, 1, 4, -3, -1, 4, 5, 1, 4, 13, 19, 24, 41, 73, 116, 181, 295, 484, 781, 1257, 2036, 3301, 5339, 8632, 13969, 22609, 36580, 59181, 95759, 154948, 250709, 405649, 656356, 1062013, 1718371, 2780376, 4498745, 7279129, 11777876, 19056997, 30834871, 49891876

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) = 4, a(3) = -3.

G.f.: (-1 - 3 x^2 + 8 x^3)/(-1 + x + x^3 + x^4).

Mathematica

LinearRecurrence[{1, 0, 1, 1}, {1, 1, 4, -3}, 100]

Crossrefs

Cf. A001622, A000045.

Sequence in context: A130806 A200490 A016499 * A066204 A217537 A154278

Adjacent sequences: A295674 A295675 A295676 * A295678 A295679 A295680

Keyword

easy,sign

Author

Clark Kimberling, Nov 27 2017

Status

approved