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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, 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)