What's the number that follows in this sequence, and what is the sequence's significance?

0,1,2,9,44,265,...

Let pth term of the sequence be S(p).

In the given problem:

S(1) = 0, S(2) = 1, and:
 S(p)/(p-1) = (S(p-1) + S(p-2)), for p>2

Accordingly:

S(7)/6 = (44+265)= 309, giving: S(7) = 6*309 = 1854
S(8)/7 = (265 + 1854) = 2110, giving: S(8) = 2119*7 = 14833

Thus, the required missing terms are 1854 and 14833

** The given sequence S(p) represents the number of derangements of p objects.   
 

Edited on November 14, 2007, 4:00 am

Posted by K Sengupta on 2007-11-14 03:59:56