Find an explicit formula for the number of partitions of a positive integer $k$ into parts no larger than $2$?
I was thinking about it and worked on it, I've come up with $1^k+2^k= 3^n$.
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Eman Yalpsid
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user412248
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What does "1^k,2^k= 3^nth power" mean? – Apr 26 '17 at 21:22
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Sorry I mean to put + sign between 1+2=3 – user412248 Apr 26 '17 at 21:23
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You've come up with a false identity. And I really don't get why some people seem to have an affection for writing $1^k$ instead of $1$, when they are evidently the same thing. – Apr 26 '17 at 21:59
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So what would the formula be then? – user412248 Apr 26 '17 at 22:00
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Try some small cases and see if you recognize the numbers. There is a recurrence, as the last number added to make $k$ can be either a $1$ or a $2$. You could also look at Mark Bennet's answer here – Ross Millikan Apr 26 '17 at 23:21
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-amWhy so it would be P_k+1=P_k+P_k-1=F_k+1+F_k by= F_k+2 – user412248 Apr 27 '17 at 05:01