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2-2, 3-4, 4-8, 5-16, 6-31, 7-57, 8-99, 9-163, 10-256

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n-Xn,
Xn=3(Xn-1)-3(Xn-2)+(Xn-3)+n-3
For example
n=5
(X5)=3*8-3*4+2+5-3=16
and
n=11
(X11)=3*256-3*163+99+11-3=386
11--386
Problem pototype: A circle has n points, and each of the two are connected, up to the circl into several parts?

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i need to know how you got that answer? how did u come up with that ? ('
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a2-a1=b1=1

.......

an-a(n-1)=b(n-1)=?

b2-b1=c1=1

.........

b(n-1)-b(n-2)=c(n-2)=?

c2-c1=1

c3-c2=2

c4-c3=3

.........

c(n-2)-c(n-3)=n-3

c(n-2)-c1=(n-2)(n-3)/2

c(n-2)=1/2n²-5/2n+4,

b(n-1)-b1=1/2(3²+4²+...+n²)-5/2(3+...+n)+4(n-2)

=1/12n(n+1)(2n+1)-5/2-5/2(1+n)n/2+15/2+4(n-2)

b(n-1)=1/6n³-1/6n²-1/6n-4(n-1)=1/6n³-n²+17/6n-2

an-a1=1/6(1+2³+...+n³)-1/6-(1+2²+3²+..+n²)+1+17/6(1+...+n)-17/6-2(n-1)

=1/6(1/2n(n+1))²-1/6n?n+1)(2n+1)+17/12n(n+1)-2n

an=1/24n^4-1/4n^3+23/24*n^2-3/4n+1;
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oh my gaawd ... you are smart ! :D
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Thank you!
I major in Mathematics,and I happen to know the answer.
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