From: Skouteris Dimitris (dimitris(@)impact.dyn.unipg.it)
Date: Δευ 31 Μαρ 2003 - 11:10:58 EEST
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Kalhmera se olous. Gia na doume loipon...
Thn pi0anothta P(n) na mhn exoun er0ei pou0ena duo korwnes sunexomenes se n riyeis th grafoume ws phliko twn eunoikwn pros ta dunata apotelesmata.
Ta dunata apotelesmata profanws einai 2^n ton ari0mo.
Estw E(n) ta eunoika apotelesmata. Uparxoun duo eidh eunoikwn apotelesmatwn.
- Auta sta opoia h n-osth riyh efere grammata [ E(n-1) ton ari0mo, afou to mono pou 0eloume einai oi prwtes n-1 riyeis na mhn exoun sunexomenes korwnes].
- Auta sta opoia h n-osth riyh efere korwna kai kata sunepeia h (n-1)-osth efere grammata [ E(n-2) ton ari0mo, afou twra to mono pou 0eloume einai oi prwtes n-2 na mhn exoun sunexomenes korwnes].
Dhladh E(n) = E(n-1) + E(n-2) gia n>2.
Epishs profanws E(1) = 2, E(2) = 3. Dhladh E(3) = 5, E(4) = 8, E(5) = 13 klp.
Me duo logia E(n) = F(n+2), o (n+2)-ostos oros ths gnwsths kai agaphmenhs mas akolou0ias Fibonacci pou parousiasthke sth lista kati evdomades prin (h akolou0ia 1,1,2,3,5,8,13,... pou o ka0e oros ths dinetai apo to a0roisma twn duo prohgoumenwn).
Opote P(n) = F(n+2) / 2^n
Epituxontes :
George Papargiris
Athanasios N. Nikolakopoulos
Kala na pernate,
Dimitris
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