Shining Star Sequence?

if there is 1dot, then 8dots, forming a star, then 21 star, how many star would there be on the 10th and wat is the formula for that.

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A few days ago

brashion

Favorite Answer

1, 8, 21, 40, 65, 96, 133, 176, 225, 280

The formula for s(n) is

[(3n-2)(3n-1)(3n)] / [(3n-2)+(3n-1)+(3n)]

which could be simplfied, but is easier this way: the product of three numbers over the sum of those same numbers. E.g., for n = 10, you have

(28*29*30) / (28+29+30) = 24360 / 87 = 280

More info at

http://www.research.att.com/~njas/sequences/A000567

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