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Search: id:A091650
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| A091650 |
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Let M = the 4 X 4 matrix [0 1 0 0 / 0 0 1 0 / 0 0 0 1 / -1 -1 3 2]. Set seed vector = [1 1 1 1] = first row, then take M*[1 1 1 1] = [1 1 1 3] then M * [1 1 1 3], etc. Sequence gives terms in rightmost column. |
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+0
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| 1, 3, 7, 21, 59, 171, 491, 1415, 4073, 11729, 33771, 97241, 279993, 806209, 2321385, 6684163, 19246279, 55417453
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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 a 9-Gon diagonal.
1. The other 3 columns are offsets of 1, 3, 7, 21, 59, ... starting with 1's. 2. The characteristic equation of the 4 X 4 matrix is x^4 - 2x^3 - 3x^4 + x + 1 (coefficients may be found in A066170) with roots 2.879385241..., -1, -.5320888862... and .65270364466...An alternative matrix giving the same eigenvalues (refer to A046854) relates to the 9-Gon: [1 1 1 1 / 1 1 1 0 / 1 1 0 0 / 1 0 0 0] since the eigenvalue 2.8793852...is the longest diagonal of the 9-Gon given edge = 1. Or, 2.879385... = 1/(2Cos k*Pi/9), k = 4.
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EXAMPLE
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a(5) = 59 since M*[1 1 1 1] then 4 iterates = [3 7 21 59]. a(5) = rightmost term.
a(10)/a(9) = 11729/4073 = 2.8796955...
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CROSSREFS
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Cf. A066170, A046854.
Sequence in context: A091489 A047087 A104779 this_sequence A096240 A035080 A091486
Adjacent sequences: A091647 A091648 A091649 this_sequence A091651 A091652 A091653
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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), Jan 25 2004
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