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Search: id:A100296
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| A100296 |
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Sequence generated from a symmetric matrix. |
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+0
2
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| 1, 6, 25, 111, 488, 2149, 9461, 41654, 183389, 807403, 3554736, 15650361, 68903513, 303360038, 1335596817, 5880203831, 25888648920, 113979406525, 501814720109
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OFFSET
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1,2
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COMMENT
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A100295 is generated from M^n * [1 0 0]. a(n)/a(n-1) tends to 4.4026788295...a root of the characteristic polynomial of M, x^3 - 4x^2 - 2x + 1 and an eigenvalue of M.
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FORMULA
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a(n) = rightmost term in M^n * [1 1 1]. a(n) = 4*a(n-1) + 2*a(n-2) - a(n-3).
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EXAMPLE
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a(5) = 488 since M^5 * [1 1 1] = [2149 1263 488]. 2149 = a(6).
a(8) = 4*a(7) + 2*a(6) - a(5) =41654 = 4*9461 + 2*2149 - 488.
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CROSSREFS
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Cf. A100295.
Adjacent sequences: A100293 A100294 A100295 this_sequence A100297 A100298 A100299
Sequence in context: A029871 A048875 A094669 this_sequence A120758 A099359 A073967
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoogroups.com), Nov 11 2004
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