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A045925
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n*Fibonacci(n).
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14
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0, 1, 2, 6, 12, 25, 48, 91, 168, 306, 550, 979, 1728, 3029, 5278, 9150, 15792, 27149, 46512, 79439, 135300, 229866, 389642, 659111, 1112832, 1875625, 3156218, 5303286, 8898708, 14912641, 24961200, 41734339, 69705888, 116311074
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of levels in all compositions of n+1 with only 1's and 2's.
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LINKS
| S. Heubach and T. Mansour, Counting rises, levels and drops in compositions
Index to sequences with linear recurrences with constant coefficients, signature (2,1,-2,-1).
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FORMULA
| G.f.: x*(1+x^2)/(1-x-x^2)^2.
G.f.: Sum_{n>=1} phi(n)*fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) = Sum_{n>=1} n*fibonacci(n)*x^n, where phi(n) = A000010(n) and Lucas(n) = A000204(n). [From Paul D. Hanna, Jan 12 2012]
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MATHEMATICA
| Table[Fibonacci[n]*n, {n, 0, 33}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 09 2009]
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PROG
| (MAGMA) [n*Fibonacci(n): n in [0..60]]; // Vincenzo Librandi, Apr 23 2011
(PARI) {Lucas(n)=fibonacci(n-1)+fibonacci(n+1)}
{a(n)=polcoeff(sum(m=1, n, eulerphi(m)*fibonacci(m)*x^m/(1-Lucas(m)*x^m+(-1)^m*x^(2*m)+x*O(x^n))), n)} /* Paul D. Hanna, Jan 12 2012 */
(PARI) a(n)=n*fibonacci(n) \\ Charles R Greathouse IV, Jan 12 2012
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CROSSREFS
| Partial sums: A014286. Cf. A000045.
Sequence in context: A034882 A175943 A137829 * A128020 A116562 A140659
Adjacent sequences: A045922 A045923 A045924 * A045926 A045927 A045928
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KEYWORD
| nonn,easy
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AUTHOR
| Jeff Burch (gburch(AT)erols.com)
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EXTENSIONS
| Incorrect formula removed by Gary Detlefs, Oct 27 2011
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