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A295726
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a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 1, a(3) = 1.
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1
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0, -1, 1, 1, 6, 9, 23, 36, 75, 119, 226, 361, 651, 1044, 1823, 2931, 5010, 8069, 13591, 21916, 36531, 58959, 97538, 157521, 259155, 418724, 686071, 1108891, 1811346, 2928429, 4772543, 7717356, 12555435, 20305559, 32992066, 53363161, 86617371, 140111604
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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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Clark Kimberling, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (1, 3, -2, -2)
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FORMULA
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a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0, a(1) = -1, a(2) = 1, a(3) = 1.
G.f.: (-x + 2 x^2 + 3 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}, {0, -1, 1, 1}, 100]
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CROSSREFS
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Cf. A001622, A000045, A005672.
Sequence in context: A033705 A033704 A121592 * A034718 A215528 A155577
Adjacent sequences: A295723 A295724 A295725 * A295727 A295728 A295729
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KEYWORD
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easy,sign
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AUTHOR
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Clark Kimberling, Nov 29 2017
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STATUS
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approved
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