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

Author

Jeremy Dover, Sep 25 2017

Keywords

• nonn
• tabl

Examples

			  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.

Formula

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