A292998 Number of sequences of balls colored with at most n colors such that exactly three balls are the same color as some other ball in the sequence.
1, 10, 87, 772, 7285, 74046, 812875, 9626632, 122643657, 1675253170, 24449818591, 379984902540, 6268557335677, 109443030279142, 2016658652491155, 39119860206021136, 797013832285599505, 17017679492994949722, 380045072079456330727
Offset: 1
Keywords
Examples
For n=2 colors a, b, the a(n)=10 sequences of balls are: aaa, bbb, abbb, babb, bbab, bbba, baaa, abaa, aaba, aaab.
Links
- Jeremy M. Dover, Repetition in Colored Sequences of Balls, arXiv:1710.06049 [math.CO], 2017.
Programs
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Mathematica
Table[n!*Sum[Binomial[k, 3]/(n + 2 - k)!, {k, 3, n + 2}], {n, 19}] (* Michael De Vlieger, Sep 28 2017 *) -
PARI
a(n) = n! * sum(k=3, n+2, binomial(k,3)/(n+2-k)!); \\ Michel Marcus, Sep 29 2017
Formula
a(n) = n! * Sum_{k=3..n+2} binomial(k,3)/(n+2-k)!.
Comments