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A298158 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, 1, 1, 10, 15, 41, 64, 137, 217, 418, 667, 1213, 1944, 3413, 5485, 9410, 15151, 25585, 41248, 68881, 111153, 184130, 297331, 489653, 791080, 1297117, 2096389, 3426274, 5539047, 9030857, 14602672, 23764601, 38432809, 62459554, 101023435, 164007277 (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 - x + 6 x^2 + 4 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.

Sequence in context: A320576 A153731 A262226 * A154989 A064307 A165883

Adjacent sequences:  A298155 A298156 A298157 * A298159 A298160 A298161

KEYWORD

easy,sign

AUTHOR

Clark Kimberling, Feb 09 2018

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)