A295671 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 1, a(3) = -1.

1, 1, 1, -1, 1, 3, 3, 3, 7, 13, 19, 29, 49, 81, 129, 207, 337, 547, 883, 1427, 2311, 3741, 6051, 9789, 15841, 25633, 41473, 67103, 108577, 175683, 284259, 459939, 744199, 1204141, 1948339, 3152477, 5100817, 8253297, 13354113, 21607407, 34961521, 56568931

Offset

0,6

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) = -1.

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

Mathematica

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

Crossrefs

Cf. A001622, A000045.

Sequence in context: A137438 A098524 A143015 * A107709 A111521 A177937

Adjacent sequences: A295668 A295669 A295670 * A295672 A295673 A295674

Keyword

easy,sign

Author

Clark Kimberling, Nov 27 2017

Status

approved