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A295853 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = -1, a(2) = 2, a(3) = 1. 1
-2, -1, 2, 1, 13, 14, 47, 61, 148, 209, 437, 646, 1243, 1889, 3452, 5341, 9433, 14774, 25487, 40261, 68308, 108569, 181997, 290566, 482803, 773369, 1276652, 2050021, 3367633, 5417654, 8867207, 14284861, 23315908, 37600769, 61244357, 98845126, 160744843 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
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
FORMULA
a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = -2, a(1) = -1, a(2) = 2, a(3) = 1.
G.f.: (-2 + x + 9 x^2 - 2 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {-2, -1, 2, 1}, 100]
CROSSREFS
Sequence in context: A134304 A211096 A134569 * A287541 A288196 A072883
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Dec 01 2017
STATUS
approved

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Last modified June 13 05:35 EDT 2024. Contains 373366 sequences. (Running on oeis4.)