A295678 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 1, a(3) = 3.

1, 2, 1, 3, 6, 9, 13, 22, 37, 59, 94, 153, 249, 402, 649, 1051, 1702, 2753, 4453, 7206, 11661, 18867, 30526, 49393, 79921, 129314, 209233, 338547, 547782, 886329, 1434109, 2320438, 3754549, 6074987, 9829534, 15904521, 25734057, 41638578, 67372633, 109011211

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) = 1, a(3) = 3.

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

5*a(n) = A022098(n)+2*( A000034(n+1)*(-1)^floor(n/2)). - R. J. Mathar, Apr 26 2022

Mathematica

LinearRecurrence[{1, 0, 1, 1}, {1, 2, 1, 3}, 100]

Crossrefs

Cf. A001622, A000045.

Sequence in context: A050043 A113396 A294284 * A057925 A086964 A076242

Adjacent sequences: A295675 A295676 A295677 * A295679 A295680 A295681

Keyword

nonn,easy

Author

Clark Kimberling, Nov 27 2017

Status

approved