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A292930 Triangle read by rows: T(n,k) (n>=1, 3<=k<=n+2) is the number of k-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
1, 2, 8, 3, 24, 60, 4, 48, 240, 480, 5, 80, 600, 2400, 4200, 6, 120, 1200, 7200, 25200, 40320, 7, 168, 2100, 16800, 88200, 282240, 423360, 8, 224, 3360, 33600, 235200, 1128960, 3386880, 4838400, 9, 288, 5040, 60480, 529200, 3386880, 15240960, 43545600, 59875200, 10, 360, 7200, 100800, 1058400, 8467200, 50803200, 217728000, 598752000, 798336000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Note that the three matching balls are necessarily the same color.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

T(n, k) = binomial(k,3)*n!/(n+2-k)!.

EXAMPLE

n=1 => AAA -> T(1,3)=1;

n=2 => AAA,BBB -> T(2,3)=2;

       AAAB,AABA,ABAA,BAAA,BBBA,BBAB,BABB,ABBB -> T(2,4)=8.

Triangle begins:

  1;

  2, 8;

  3, 24, 60;

  4, 48, 240, 480;

  5, 80, 600, 2400, 4200;

  ...

PROG

(PARI) T(n, k) = binomial(k, 3)*n!/(n+2-k)!;

tabl(nn) = for (n=1, nn, for (k=3, n+2, print1(T(n, k), ", ")); print()); \\ Michel Marcus, Sep 29 2017

CROSSREFS

Columns of table: T(n,3) = A000027(n), T(n,4) = A033996(n).

Other sequences in table: T(n,n+2) = A005990(n+1).

Sequence in context: A153188 A193976 A264244 * A126951 A282637 A256411

Adjacent sequences:  A292927 A292928 A292929 * A292931 A292932 A292933

KEYWORD

nonn,tabl

AUTHOR

Jeremy Dover, Sep 26 2017

STATUS

approved

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)