A295672 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 1, a(3) = -2.

1, 1, 1, -2, 0, 2, 1, -1, 1, 4, 4, 4, 9, 17, 25, 38, 64, 106, 169, 271, 441, 716, 1156, 1868, 3025, 4897, 7921, 12814, 20736, 33554, 54289, 87839, 142129, 229972, 372100, 602068, 974169, 1576241, 2550409, 4126646, 6677056, 10803706, 17480761, 28284463

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

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A336915 A236627 A116664 * A308074 A024161 A035156

Adjacent sequences: A295669 A295670 A295671 * A295673 A295674 A295675

Keyword

easy,sign

Author

Clark Kimberling, Nov 27 2017

Status

approved