What is S(20,3) and how do you solve it? Please and thanks!?

Update:

S has to do with partitions.

S(n,k)= S(n-1,k-1)+kS(n-1,k)

where S(n,1)=1, S(n,n)=1 and S(n,0)=0

and when k>n=0

I can never get that

2 Answers

Relevance
  • 10 years ago
    Favorite Answer

    S(20, 3)

    = S(19, 2) + 3 S(19, 3)

    = S(18, 1) + 2 S(18, 2) + 3 S(18, 2) + 9 S(18, 3)

    = S(18, 1) + 5 S(18, 2) + 9 S(18, 3)

    = 1 + 5 S(18, 2) + 9 S(18, 3)

    = 1 + 5 S(17, 1) + 10 S(17, 2) + 9 S(17, 2) + 27 S(17, 3)

    = 1 + 5 S(17, 1) + 19 S(17, 2) + 27 S(17, 3)

    = 1 + 5 + 19 S(17, 2) + 27 S(17, 3)

    = 6 + 19 S(17, 2) + 27 S(17, 3)

    = 6 + 19 S(16, 1) + 38(16, 2) + 27(16, 2) + 81 S(16, 3)

    = 6 + 19 + 38 S(16, 2) + 27 S(16, 2) + 81 S(16, 3)

    = 25 + 65 S(16, 2) + 81 S(16, 3)

    = ...

    You got the idea now? I think the answer should be around 10 septillion.

  • Ed I
    Lv 7
    10 years ago

    What is S?

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