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A023607
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a(n) = n * Fibonacci(n+1).
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19
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0, 1, 4, 9, 20, 40, 78, 147, 272, 495, 890, 1584, 2796, 4901, 8540, 14805, 25552, 43928, 75258, 128535, 218920, 371931, 630454, 1066464, 1800600, 3034825, 5106868, 8580897, 14398412, 24129160, 40388070, 67527579, 112786496, 188195271
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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Convolution of Fibonacci numbers and Lucas numbers.
a(n) = central term of the triangle in A119457 for n>0. - Reinhard Zumkeller, May 20 2006
d/dx(1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + ...) = (1 + 4x + 9x^2 + ...). - Gary W. Adamson, Jun 27 2009
For n > 0: sums of rows of the triangle in A108035. - Reinhard Zumkeller, Oct 08 2012
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
M. Griffiths, A Restricted Random Walk defined via a Fibonacci Process, Journal of Integer Sequences, Vol. 14 (2011), #11.5.4.
M. Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8, section 3.
Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).
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FORMULA
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O.g.f.: x(2x+1)/(1-x-x^2)^2. - Len Smiley, Dec 11 2001
a(n) = n*Sum_{k=0..n} binomial(k,n-k). - Paul Barry, Sep 25 2004
a(n) = A215082(2n-2) + A215082(2n-1). - Philippe Deléham, Aug 03 2012
a(n) = Sum_{i=1..n} A000045(i)*A000032(n-i+1). - Vladimir Kruchinin, Nov 08 2013
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MAPLE
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A023607 := proc(n)
n*combinat[fibonacci](n+1) ;
end proc:
seq(A023607(n), n=0..10) ; # R. J. Mathar, Jul 15 2017
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MATHEMATICA
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Times@@@Thread[{Range[0, 50], Fibonacci[Range[51]]}] (* From Harvey P. Dale *)
Table[n*Fibonacci[n + 1], {n, 0, 50}]
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PROG
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(Haskell)
a023607 n = a023607_list !! n
a023607_list = zipWith (*) [0..] $ tail a000045_list
-- Reinhard Zumkeller, Oct 08 2012
(PARI) a(n)=n*fibonacci(n+1) \\ Charles R Greathouse IV, Sep 24 2015
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CROSSREFS
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First differences of A094584.
Second column of triangle A016095.
Cf. A000045, A104796.
Sequence in context: A049748 A268235 A192956 * A117074 A072934 A084639
Adjacent sequences: A023604 A023605 A023606 * A023608 A023609 A023610
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling
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EXTENSIONS
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Simpler description from Samuel Lachterman (slachterman(AT)fuse.net), Sep 19 2003
Name improved by T. D. Noe, Mar 08 2011
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STATUS
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approved
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