[seqfan] Re: Number of n-digit numbers the binary expansion of which contains k runs of 1's

Alois Heinz heinz at hs-heilbronn.de
Fri Jul 30 18:15:26 CEST 2010

Both new sequences (A179867, A179868) should be deleted.

C(n,5) and C(n,6) here gives the number of ways to choose the positions 
of the
leftmost 1 (leftmost 0) of the first, second, third run of 1's (0's) of 
the n digit
binary number.


Charles Greathouse schrieb:
> Sum{i=2,n-3})C(i,2)*C(n-i-1,2) is just binomial(n, 5) =
> n*(n-1)*(n-2)*(n-3)*(n-4)/120.  So assuming the formula is correct,
> a(12) needs to be corrected and the keyword easy should be added.
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University

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