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A295731
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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) = 0, a(3) = 1.
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1
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-1, -1, 0, 1, 5, 10, 23, 41, 80, 137, 249, 418, 731, 1213, 2072, 3413, 5741, 9410, 15663, 25585, 42272, 68881, 113201, 184130, 301427, 489653, 799272, 1297117, 2112773, 3426274, 5571815, 9030857, 14668208, 23764601, 38563881, 62459554, 101285579, 164007277
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OFFSET
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0,5
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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) = -1, a(2) = 0, a(3) = 1.
G.f.: (-1 + 4 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, 0, 1}, 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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