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Search: id:A023607
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| A023607 |
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n*F_n, where F_n is the n-th Fibonacci number indexed F_0 = F_1 = 1. |
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+0
7
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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; listen)
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OFFSET
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0,3
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COMMENT
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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 (reinhard.zumkeller(AT)gmail.com), May 20 2006
d/dx(1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + ...) = (1 + 4x + 9x^2 + ...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 27 2009]
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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 (pbarry(AT)wit.ie), Sep 25 2004
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MAPLE
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a:=n->sum(fibonacci(n), j=2..n): seq(a(n), n=1..34); ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007
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CROSSREFS
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First differences of A094584.
Second column of triangle A016095.
Sequence in context: A009910 A060494 A049748 this_sequence A117074 A072934 A084639
Adjacent sequences: A023604 A023605 A023606 this_sequence 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 (ck6(AT)evansville.edu)
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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 (deutsch(AT)duke.poly.edu), Feb 20 2004
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