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A100297
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Sequence generated from a symmetric matrix composed of Catalan numbers.
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0
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1, 6, 89, 1430, 23070, 372259, 6006853, 96927945, 1564051382, 25237889117, 407244323586
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)/a(n-1) tends to 16.136227625...an eigenvalue of M and a root of the characteristic polynomial x^3 - 17x^2 + 14x - 1.
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FORMULA
| a(n) = leftmost term in M^n * [1 0 0], where M = the 3 X 3 matrix [1 1 2 / 1 2 5 / 2 5 14]. a(n) = 17*a(n-1) - 14*a(n-2) + a(n-3).
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EXAMPLE
| a(4) = 1430 since M^4 * [1 0 0] = [1430 3338 9151].
a(6) = 372259 = 17*23070 - 14*1430 + 89 = 17*a(5) - 14*a(4) + a(3).
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CROSSREFS
| Sequence in context: A127183 A054952 A101148 * A177568 A177573 A166782
Adjacent sequences: A100294 A100295 A100296 * A100298 A100299 A100300
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 11 2004
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