A295674 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 8.

1, 2, 4, 8, 11, 17, 29, 48, 76, 122, 199, 323, 521, 842, 1364, 2208, 3571, 5777, 9349, 15128, 24476, 39602, 64079, 103683, 167761, 271442, 439204, 710648, 1149851, 1860497, 3010349, 4870848, 7881196, 12752042, 20633239, 33385283, 54018521, 87403802

Offset

0,2

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) = 2, a(2) = 4, a(3) = 8.

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

Mathematica

LinearRecurrence[{1, 0, 1, 1}, {1, 2, 4, 8}, 100]

Crossrefs

Cf. A001622, A000045.

Sequence in context: A279097 A279098 A010068 * A120632 A007295 A053439

Adjacent sequences: A295671 A295672 A295673 * A295675 A295676 A295677

Keyword

nonn,easy

Author

Clark Kimberling, Nov 27 2017

Status

approved