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Search: id:A136421
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| A136421 |
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Floor((x^n - (1-x)^n)/sqrt(2)+.5) where x = (sqrt(2)+1)/2. |
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+0
1
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| 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6, 7, 8, 10, 12, 14, 17, 21, 25, 31, 37, 44, 54, 65, 78, 94, 114, 138, 166, 200, 242, 292, 352, 425, 514, 620, 748, 903, 1090, 1316, 1589, 1918, 2315, 2794, 3373, 4072, 4915, 5933, 7162, 8645, 10436, 12597, 15206, 18355, 22156, 26745
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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This is analogous to the closed form of the formula for the n-th Fibonacci number. Even before truncation, these numbers are rational and the decimal part always ends in 5. For x=(sqrt(2)+1)/2, a(n)/a(n-1) -> x.
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FORMULA
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The general form of x is (sqrt(r)+1)/2, r=1,2,3...
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PROGRAM
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(PARI) g(n, r) = for(m=1, n, print1(fib(m, r)", ")) fib(n, r) = x=(sqrt(r)+1)/2; floor((x^n-(1-x)^n)/sqrt(r)+.5)
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CROSSREFS
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Adjacent sequences: A136418 A136419 A136420 this_sequence A136422 A136423 A136424
Sequence in context: A033295 A018049 A120170 this_sequence A016085 A018122 A074732
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Apr 01 2008
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