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Search: id:A085503
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| A085503 |
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Horadam sequence (0,1,5,5). |
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+0
1
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| 0, 1, 5, 35, 175, 1025, 6000, 35125, 205625, 1203750, 7046875, 41253125, 241500000, 1413765625, 8276328125, 48450468750, 283633984375, 1660422265625, 9720281250000, 56903517578125, 333118994140625
(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 (5 + (3 * 5^1/2)) / 2 as n approaches infinity. (5 + (3 * 5^1/2)) / 2 can also be written as Phi^2 + (2 * Phi), Phi^3 + Phi, Phi + 5^1/2 + 2, (3 * Phi) + 1, (3 * Phi^2) - 2, Phi^4 - 1, and (5 + (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 = 5, r = 5
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EXAMPLE
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a(4) = 175 because a(3) = 30, a(2) = 5, s = 5, r = 5 and (5 * 30) + (5 * 5) = 175.
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CROSSREFS
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Cf. A024318, A000032, A000129, A001076, A085939.
Sequence in context: A097872 A124793 A048515 this_sequence A100739 A043014 A002737
Adjacent sequences: A085500 A085501 A085502 this_sequence A085504 A085505 A085506
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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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