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Search: id:A136423
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| A136423 |
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Floor((x^n - (1-x)^n)/2 +.5) where x = (sqrt(4)+1)/2 = 3/2. |
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+0
1
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| 1, 1, 2, 3, 4, 6, 9, 13, 19, 29, 43, 65, 97, 146, 219, 328, 493, 739, 1108, 1663, 2494, 3741, 5611, 8417, 12626, 18938, 28408, 42611, 63917, 95876, 143813, 215720, 323580, 485370, 728055, 1092082, 1638123, 2457185, 3685777, 5528666, 8292999
(list; graph; listen)
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OFFSET
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1,3
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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(4)+1)/2=3/2, 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: A136420 A136421 A136422 this_sequence A136424 A136425 A136426
Sequence in context: A101913 A121653 A061418 this_sequence A078932 A117791 A022860
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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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