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A295736 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -2, a(2) = -2, a(3) = 1. 1
1, -2, -2, 1, -3, 8, 1, 29, 22, 91, 97, 268, 333, 761, 1030, 2111, 3013, 5764, 8521, 15565, 23574, 41699, 64249, 111068, 173269, 294577, 463750, 778807, 1234365, 2054132, 3272113, 5408165, 8647510, 14219515, 22801489, 37348684, 60019101, 98023145, 157780102 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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, 3, -2, -2)

FORMULA

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

G.f.: (1 - 3 x - 3 x^2 + 11 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

MATHEMATICA

LinearRecurrence[{1, 3, -2, -2}, {1, -2, -2, 1}, 100]

CROSSREFS

Cf. A001622, A000045, A005672.

Sequence in context: A122941 A297622 A059584 * A136203 A113326 A262157

Adjacent sequences:  A295733 A295734 A295735 * A295737 A295738 A295739

KEYWORD

easy,sign

AUTHOR

Clark Kimberling, Nov 30 2017

STATUS

approved

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Last modified January 20 18:38 EST 2022. Contains 350472 sequences. (Running on oeis4.)