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Mathematica -count a value

Posted 10 years ago

I have a questions.

Let:`s[1]=3, s[2]=5, t[1]=1, s[n_] := t[n - 1] - t[n - 2] + 4,
t[n_] := t[n - 1] + s[n - 1]` and I must count t[100]. 

Mathematica all the time counts, but does not give the result. Thank you in advance for your help.

POSTED BY: Artur Smura
2 Replies

What you are seeing (well, not seeing) is exponential computational complexity.

Clear[s, t]
s[1] = 3;
s[2] = 5;
t[1] = 1;
s[n_] := t[n - 1] - t[n - 2] + 4
t[n_] := t[n - 1] + s[n - 1]
Table[Timing[t[n]], {n, 10, 30, 5}]

(* Out[257]= {{0., 100}, {0.012000, 225}, {0.208000, 400}, {4.396000,  625}, {92.460000, 900}} *)

For one remedy, see tutorial/FunctionsThatRememberValuesTheyHaveFound in the documentation center. Other approaches would include doing explicit iterations or recasting as a matrix power.

POSTED BY: Daniel Lichtblau
Posted 10 years ago

I understand. Thank You.

POSTED BY: Artur Smura
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