SM-5-Exercise7

4129 days ago by dmanna

#sequence A(l,m) l,m = var('l,m') def A(l,m): sum=0 for k in range(l,m+1): sum = sum + factorial(l)*factorial(m)/2^(m-l)*2^k*binomial(2*(m-k),m-k)*binomial(m+k,m)*binomial(k,l) return sum 
       
# p-adic valuation of an integer n def nu(p,n): out=oo if n!=0: out=0 while n%p==0: out=out+1 n=n/p return out 
       
#creating a list-type sequence of the first N p-adic valuations of {A_{l,m} m>=l} for given l def Seq(p,l,N): list=[] for j in range(N): list.append(nu(p,A(l,l+j))) return list 
       
#creates a plot of the previous sequence. I have the options set to connect the dots and make the plot black. def PlotSeq(p,l,N): return list_plot(Seq(p,l,N),plotjoined=True,rgbcolor=(0,0,0)) 
       
#On the next three lines, some examples: PlotSeq(2,18,100) 
       
PlotSeq(2,53,200) 
       
PlotSeq(3,40,100)