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

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

(In reply to Answer To The Problem by K Sengupta)

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

Then, the terms of the given sequence is defined by the recurrence relation:

S(p) = (p-1)(S(p-2) + S(p-1))

Thus,

S(1) = 0

S(2) = 1

S(3) = 2(0+1) = 2

S(4) = 3(1+2) = 9

S(5) = 4(2+9) = 44

S(6) = 5(9+44) = 265

S(7) = 6(44+265) = 1854

S(8) = 7(265 + 1854) = 14833

Consequently, the required missing terms are 1854 and 14833

 

Posted by K Sengupta on 2008-03-28 12:34:03