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A023607 n * Fibonacci(n+1). 19
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)
OFFSET

0,3

COMMENTS

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

LINKS

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.

Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).

FORMULA

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

MAPLE

with (combinat): a:= n-> sum(fibonacci(n+1), j=1..n): seq(a(n), n=0..34); - Zerinvary Lajos, Apr 25 2007

MATHEMATICA

Times@@@Thread[{Range[0, 50], Fibonacci[Range[51]]}]  (* From Harvey P. Dale *)

Table[n*Fibonacci[n + 1], {n, 0, 50}]

PROG

(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

CROSSREFS

First differences of A094584.

Second column of triangle A016095.

Cf. A000045.

Sequence in context: A049748 A268235 A192956 * A117074 A072934 A084639

Adjacent sequences:  A023604 A023605 A023606 * A023608 A023609 A023610

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Simpler description from Samuel Lachterman (slachterman(AT)fuse.net), Sep 19 2003

Name improved by T. D. Noe, Mar 08 2011

STATUS

approved

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Last modified March 25 21:19 EDT 2017. Contains 284111 sequences.