I cannot see were this relation is to be seen on this graph It looks more like P(n) =P(n-1) + P(floor(n/2)) Do both formulas lead to the..
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P(n)=P(n-2)+P(n-3) (P(n-4)+P(n-5))+P(n-3) P(n-1)+P(n-5)
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P(n)=P(n-1)+P(n-5) too as you can see in the triangle spiral and by expending P(n-2) and then combing terms to create P(n-1)
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We did a fun project for kids a while back on this spiral using our Zometool set:https://mikesmathpage.wordpress.com/2017/01/31/the-plastic-number/ …
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That kind of stuff tells me the world is ok. In fact, it tells me, the world can go eat its own hat. Maths is the language of happiness
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