I can't find the starting points.
Thank you for your help.
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2What have you tried? Try to compute the first terms of your sequence, and then make a conjecture. – Crostul Jun 14 '15 at 09:08
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The starting points are $f(0)={0 \choose 0}=1$ and $f(1)={1 \choose 0}=1$ – Henry Jun 14 '15 at 09:18
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Is it the Fibonacci Numbers? – c-301 Jun 14 '15 at 10:00
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No, they aren't. – Jun 14 '15 at 12:07
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I want to find the closed form of $\sum\limits_{i=0}^{\lfloor n/2\rfloor}{n-i\choose i}$ - And I want to drive a Rolls Royce, for instance. :-$)$ – Lucian Jun 14 '15 at 12:37
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1@G.Sassatelli: yes they are. – Jack D'Aurizio Jun 14 '15 at 12:43
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Sorry, @JackD'Aurizio, I misread the question. – Jun 14 '15 at 12:45
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Prove by induction that: $$ \sum_{i=0}^{n}\binom{2n-i}{i}=F_{2n+1} $$ or just look here, then adjust your formula to cover the remaining cases.
Jack D'Aurizio
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