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A023607
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n * Fibonacci(n+1).
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16
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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
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refs;
listen;
history;
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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 + ...). [From 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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REFERENCES
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M. Griffiths, A Restricted Random Walk defined via a Fibonacci Process, Journal of Integer Sequences, Vol. 14 (2011), #11.5.4.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..1000
Index to sequences with 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 (smiley(AT)math.uaa.alaska.edu), 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
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MAPLE
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with (combinat): a:= n-> sum(fibonacci(n+1), j=1..n): seq(a(n), n=0..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007
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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
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CROSSREFS
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First differences of A094584.
Second column of triangle A016095.
Cf. A000045.
Sequence in context: A060494 A049748 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
More terms from Emeric Deutsch, Feb 20 2004
Name improved by T. D. Noe, Mar 08 2011
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STATUS
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approved
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