A295673 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 4, a(1) = 3, a(2) = 2, a(3) = 1.

4, 3, 2, 1, 8, 13, 16, 25, 46, 75, 116, 187, 308, 499, 802, 1297, 2104, 3405, 5504, 8905, 14414, 23323, 37732, 61051, 98788, 159843, 258626, 418465, 677096, 1095565, 1772656, 2868217, 4640878, 7509099, 12149972, 19659067, 31809044, 51468115, 83277154

Offset

0,1

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) = 4, a(1) = 3, a(2) = 2, a(3) = 1.

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

Mathematica

LinearRecurrence[{1, 0, 1, 1}, {4, 3, 2, 1}, 100]

Crossrefs

Cf. A001622, A000045.

Sequence in context: A370350 A194743 A113778 * A155172 A253902 A349727

Adjacent sequences: A295670 A295671 A295672 * A295674 A295675 A295676

Keyword

easy,nonn

Author

Clark Kimberling, Nov 27 2017

Status

approved