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Search: id:A100059
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| 1, 5, 14, 45, 139, 434, 1351, 4209, 13110, 40837, 127203, 396226, 1234207, 3844441, 11975078, 37301261, 116189979, 361921042, 1127350583, 3511592833, 10938286998, 34071752661, 106130359315, 330586256610
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OFFSET
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1,2
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COMMENT
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a(n)/a(n-1) tends to 3.11490754148...an eigenvalue of M and a root of the characteristic polynomial x^3 - 3x^2 - x + 2.
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REFERENCES
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Boris A. Bondarenko, "Generalized Pascal Triangles and Pyramids, Their Fractals, Graphs, and Applications"; Fibonacci Association, 1993, p. 27.
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FORMULA
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G.f.: x(1+2x-2x^3)/(1-3x+x^2-2x^3).
Recurrence: a(n) = 3*a(n-1) + a(n-2) - 2*a(n-3).
a(n) = rightmost term in M^5 * [1 1 1], where M = the 3 X 3 upper triangular matrix [2 1 2 / 1 1 0 / 1 0 0].
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EXAMPLE
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a(5) = 139 = rightmost term in M^5 * [1 1 1] which is [434 205 139]. 434 = a(6), while 205 = A052911(5).
a(6) = 434 = 3*a(5) + a(4) - 2*a(3) = 3*139 + 45 - 2*14.
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CROSSREFS
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Cf. A019481, A052550, A052939, A100058, A058071.
Adjacent sequences: A100056 A100057 A100058 this_sequence A100060 A100061 A100062
Sequence in context: A034530 A125246 A140796 this_sequence A077335 A126729 A098730
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 31 2004
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EXTENSIONS
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Edited by Ralf Stephan, Nov 02 2004
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