A295680 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0, a(1) = 0, a(2) = 0, a(3) = 2.

0, 0, 0, 2, 2, 2, 4, 8, 12, 18, 30, 50, 80, 128, 208, 338, 546, 882, 1428, 2312, 3740, 6050, 9790, 15842, 25632, 41472, 67104, 108578, 175682, 284258, 459940, 744200, 1204140, 1948338, 3152478, 5100818, 8253296, 13354112, 21607408, 34961522, 56568930

Offset

0,4

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

a(n) = 2*A006498(n-3) for n >= 3.

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A077943 A077993 A302613 * A099768 A285636 A102831

Adjacent sequences: A295677 A295678 A295679 * A295681 A295682 A295683

Keyword

nonn,easy

Author

Clark Kimberling, Nov 27 2017

Status

approved