Find a formula to calculate G(n) and it should be a polynomial of degree 4.(adsbygoogle = window.adsbygoogle || []).push({});

G(n) = 1/6(0)(0-1)(0-2) + 1/6(1)(1-1)(1-2)+...+1/6(n-1)(n-2)(n-3)

I know

G(0)=G(1)=G(2)=G(3)=0

G(4)=1

G(5)=1+3

G(6)=1+3+6

G(7)=1+2+3+10

G(8)=1+3+6+10+15 (sum of triangle numbers)

What should I do to find out the forumla? I think it is some kind of interpolation formula.

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# Interpolation forumula

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