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Search: id:A099920
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| 0, 2, 3, 8, 15, 30, 56, 104, 189, 340, 605, 1068, 1872, 3262, 5655, 9760, 16779, 28746, 49096, 83620, 142065, 240812, 407353, 687768, 1159200, 1950650, 3277611, 5499704, 9216519, 15426870, 25793240, 43080608, 71884197, 119835652
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OFFSET
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0,2
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COMMENT
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A Fibonacci-Lucas convolution.
The number of edges in the Lucas cube L_(n+1) [Klavzar]. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 05 2008]
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 35.
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LINKS
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S. Klavzar, On median nature and enumerative properties of Fibonacci-like cubes, Discr. Math. 299 (2005), 145-153. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 05 2008]
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FORMULA
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G.f.: x(2-x)/(1-x-x^2)^2; a(n)=sum{k=0..n, F(n-k)(L(k-1)+0^k)}; a(n)=sum{k=0..n+1, F(n-k)binomial(n-k+1, k)binomial(1, (k+1)/2)(1-(-1)^k)/2}.
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MAPLE
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a:=n->sum(fibonacci(n), j=0..n): seq(a(n), n=0..32); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007
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CROSSREFS
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Equals A010049(n) + A001629(n+1).
Cf. A000045, A000032, A045925.
Sequence in context: A056802 A026698 A099428 this_sequence A128022 A011946 A080206
Adjacent sequences: A099917 A099918 A099919 this_sequence A099921 A099922 A099923
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KEYWORD
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nonn,new
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie) and Ralf Stephan, Oct 15 2004
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EXTENSIONS
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Entry revised Jan 23 2006 by njas. The offset changed, so some of the formulae may now be slightly off.
Corrected typo of A010049-number in formula. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 26 2008
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