[seqfan] Pb on A44 and A107358

Robert FERREOL ferreol at mathcurve.com
Wed Oct 4 14:44:30 CEST 2017


About A44, https://oeis.org/draft/A000044:

If the hypothesis are : there is one pair of rabbits at
       month one, and a pair of rabbit born in month n begins to
       procreate month n + 2, and continues to procreate until month n +
       12, and dies at the end of this month (each couple therefore gives
       birth to 12-2+1=11 pairs) , the sequence giving the number of
       pairs living at the end of month n is defined by :

       a(n)=0 for n<=0, a(n)=1 for 1≤n≤2, a(n)=a(n-1)+a(n-2) for
       3≤n≤12, a(n)=a(n-2)+a(n-3)+...+ a(n-12) for n≥13.

       

       Except the case n=0, this is giving this sequence and NOT A107358
       ; so A107358 is NOT a "more satisfactory version of dying rabbits"
       ; We have a(13)=232 and not fibonacci(13)=233 because at the end
       of the 13th month, the first pair is died. So for me, the right
       definition of A44 is :

       

       a(n)= Fibonacci(n) for n <= 12 ; for n≥13,
       a(n)=a(n-2)+a(n-3)+...+ a(n-12) .

       

       And we have a(n) = a(n-1)+a(n-2)-a(n-13) (consequence of
       a(n)=a(n-2)+a(n-3)+...+ a(n-12))  ONLY for n>=14 ,
       (a(13)-a(12)-a(11)=-1 and not 0 !!)

       

       

     

-- 

ROBERT FERRÉOL
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