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

N. J. A. Sloane njas at research.att.com
Sun Aug 1 06:34:02 CEST 2010


I find the definitions very confusing.

"a(n) is the number of n-digit numbers the binary expansion of which contains 3 runs of 1's"

"digit" means base 10, of course.

I think what was intended was

"a(n) is the number of n-bit binary numbers which contain 3 runs of 1's."

(the final period was omitted, by the way)

Otherwise the reader starts to think, hmmm, we are supposed to
take all n-digit decimal numbers, convert them to
binay, and look at the runs in the binary expansion.
Of course perhaps that is what was intended?
No, clearly not.

When corrected, these sequences do seem to be simply
binomial coefficients, and so are duplicates.
I will delete them. A comment could be added to
the appropriate existing entries.

Neil





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