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Search: id:A085504
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| A085504 |
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Horadam sequence (0,1,9,3). |
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+0
1
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| 0, 1, 18, 81, 405, 1944, 9477, 45927, 223074, 1082565, 5255361, 25509168, 123825753, 601059771, 2917611090, 14162371209, 68745613437, 333698181192, 1619805064509, 7862698824255
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) / a(n-1) converges to (3 + (3 * 5^1/2)) / 2 as n approaches infinity. (3 + (3 * 5^1/2)) / 2 can also be written as Phi^2 + (2 * Phi) - 1, Phi^3 + Phi - 1, Phi + 5^1/2 + 1, 3 * Phi, (3 * Phi^2) - 3, Phi^4 - 2 and (3 + (3 * (L(n) / F(n)))) / 2, where L(n) is the n-th Lucas number and F(n) is the n-th Fibonacci number as n approaches infinity.
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LINKS
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Eric Weisstein, Horadam Sequence
Eric Weisstein, Fibonacci Number
Eric Weisstein, Pell Number
Eric Weisstein, Lucas Number
Eric Weisstein, Lucas Sequence
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FORMULA
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a(n) = s*a(n-1) + r*a(n-2); for n > 1, where a(0) = 0, a(1) = 1, s = 3, r = 9
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EXAMPLE
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a(4) = 405 because a(3) = 81, a(2) = 18, s = 3, r = 9 and (3 * 81) + (9 * 18) = 405.
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CROSSREFS
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Cf. A024318, A000032, A000129, A001076, A085939.
Sequence in context: A039408 A043231 A044011 this_sequence A087636 A156218 A118293
Adjacent sequences: A085501 A085502 A085503 this_sequence A085505 A085506 A085507
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KEYWORD
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easy,nonn
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AUTHOR
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Ross La Haye (rlahaye(AT)new.rr.com), Aug 18 2003
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