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A295722
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a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -1, a(2) = 2, a(3) = 3.
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1
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-1, -1, 2, 3, 13, 20, 49, 77, 158, 251, 473, 756, 1357, 2177, 3790, 6095, 10397, 16748, 28169, 45429, 75646, 122099, 201841, 325988, 536021, 866105, 1418510, 2292807, 3744085, 6053276, 9862897, 15948941, 25942910, 41957387, 68162441, 110250900, 178937629
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OFFSET
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0,3
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COMMENTS
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a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = -1, a(1) = -2, a(2) = 2, a(3) = 3.
G.f.: (-1 + 6 x^2 + 2 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
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MATHEMATICA
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LinearRecurrence[{1, 3, -2, -2}, {-1, -1, 2, 3}, 100]
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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