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A136425
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Floor((x^n-(1-x)^n)/sqrt(7)+0.5) where x=(sqrt(7)+1)/2.
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0
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1, 1, 3, 4, 8, 14, 25, 46, 84, 153, 279, 509, 927, 1691, 3082, 5618, 10241, 18667, 34028, 62029, 113070, 206113, 375719, 684889, 1248467, 2275800, 4148501, 7562201, 13784953, 25128255, 45805684, 83498067, 152206593, 277453693, 505763582
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This is analogous to 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(7)+1)/2, a(n)/a(n-1) -> x. The general form of x is (sqrt(r)+1)/2, r=1,2,3..
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FORMULA
| Asymptotically a(n) ~ A083099(n)/2^(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 20 2008
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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: A023558 A170902 A000205 * A005907 A049866 A118355
Adjacent sequences: A136422 A136423 A136424 * A136426 A136427 A136428
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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 R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 20 2008
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