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A136424
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Floor((x^n - (1-x)^n) / (2x-1) +.5) where x = (sqrt(6)+1)/2 (and hence 2x-1 = sqrt(6)).
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1, 1, 2, 4, 6, 11, 19, 32, 55, 95, 164, 283, 488, 842, 1451, 2503, 4318, 7447, 12844, 22152, 38207, 65898, 113657, 196029, 338101, 583137, 1005763, 1734685, 2991888, 5160244, 8900104, 15350410, 26475540, 45663552, 78757977, 135837417
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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(6)+1)/2, a(n)/a(n-1) -> x.
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FORMULA
| The general form of x is (sqrt(r)+1)/2, r=1,2,3..
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PROG
| (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
| Sequence in context: A140443 A115992 A115993 * A116732 A048239 A000786
Adjacent sequences: A136421 A136422 A136423 * A136425 A136426 A136427
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Apr 01 2008
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EXTENSIONS
| Definition corrected by Frederic van der Plancke (fplancke(AT)hotmail.com), May 08 2009
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