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A295675 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 2, a(3) = -2. 1
1, 1, 2, -2, 0, 3, 3, 1, 4, 10, 14, 19, 33, 57, 90, 142, 232, 379, 611, 985, 1596, 2586, 4182, 6763, 10945, 17713, 28658, 46366, 75024, 121395, 196419, 317809, 514228, 832042, 1346270, 2178307, 3524577, 5702889, 9227466, 14930350, 24157816, 39088171 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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

MATHEMATICA

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

CROSSREFS

Cf. A001622, A000045.

Sequence in context: A048142 A071426 A288530 * A135356 A259016 A216504

Adjacent sequences:  A295672 A295673 A295674 * A295676 A295677 A295678

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.)