Determine the total number of quintuplets (A,B,C,D,E) of positive integers such that A<=B<=C<=D<=E<=N.
Both analytic and software solution for N=1, 2, ...9,10,...N required.
Q(N)=number of quintuplets
Q(N)=N(N+1)(N+2)(N+3)(N+4)/5!=(N^5+10N^4+35N^3+50N^2+24N)/120
Q(1)=1
Q(2)=6
Q(3)=21
Q(4)=56
Q(5)=126
Q(6)=252
Q(7)=462
Q(8)=792
Q(9)=1287
Q(10)=2002
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Posted by Math Man
on 2011-03-17 17:32:03 |
Solution
