A292879 Triangle read by rows: T(n,k) (n>=1, 4<=k<=n+3) is the number of k-sequences of balls colored with at most n colors such that exactly three balls are of a color seen previously in the sequence.

1, 2, 30, 3, 90, 540, 4, 180, 2160, 8400, 5, 300, 5400, 42000, 126000, 6, 450, 10800, 126000, 756000, 1905120, 7, 630, 18900, 294000, 2646000, 13335840, 29635200, 8, 840, 30240, 588000, 7056000, 53343360, 237081600, 479001600, 9, 1080, 45360, 1058400, 15876000, 160030080, 1066867200, 4311014400, 8083152000

Offset

1,2

Links

Table of n, a(n) for n=1..45.

Formula

[binomial(k,4)+10*binomial(k,5)+15*binomial(k,6)]*n!/(n+3-k)!

Example

  n=1 => AAAA -> T(1,4)=1
  n=2 => AAAA,BBBB -> T(2,4)=2
         AAAAB,AAABA,AABAA,ABAAA,BAAAA,BBBBA,BBBAB,BBABB,BABBB,ABBBB,
         AAABB,AABAB,AABBA,ABAAB,ABABA,ABBAA,BAAAB,BAABA,BABAA,BBAAA,
         BBBAA,BBABA,BBAAB,BABBA,BABAB,BAABB,ABBBA,ABBAB,ABABB,AABBB -> T(2,5)=30
Triangle begins:
1;
2,   30;
3,   90,   540;
4,  180,  2160,    8400;
5,  300,  5400,   42000,   126000;
6,  450, 10800,  126000,   756000,   1905120;
7,  630, 18900,  294000,  2646000,  13335840,   29635200;
8,  840, 30240,  588000,  7056000,  53343360,  237081600,  479001600;
...

Crossrefs

Main diagonal is A037961.

Sequence in context: A087194 A331427 A058988 * A361027 A267131 A078690

Adjacent sequences: A292876 A292877 A292878 * A292880 A292881 A292882

Keyword

nonn,tabl

Author

Jeremy Dover, Sep 25 2017

Status

approved