[seqfan] Re: Number of n-digit binary numbers containing k runs of 1's

[Alois Heinz]

Vladimir Shevelev schrieb:
>  
> Dear SeqFans,
>  
> I have just submitted two sequences (I corrected %N's)
>  
>  
> %I A179867
> %S A179867 0,0,0,0,1,6,21,56,126,252,462,522
> %N A179867 a(n) is the number of n-digit binary numbers containing 3 runs of 1's 
>   
It is the same as

A000389 Binomial coefficients C(n,5).
1, 6, 21, 56, 126, 252, 462, 792, 1287, 2002, 3003, 4368

(if computet correctly)
> %I A179868
> %S A179868 0,0,0,0,0,1,7,28,84,210,462,924,1716
> %N A179868 a(n) is the number of n-digit binary numbers containing 3 runs of 0's 
>   
The same as

A000579 Figurate numbers or binomial coefficients C(n,6).
1, 7, 28, 84, 210, 462, 924, 1716, 3003

Alois