#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
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# 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
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#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
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#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))
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#On the next three lines, some examples:
PlotSeq(2,18,100)
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PlotSeq(2,53,200)
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PlotSeq(3,40,100)
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