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Monday, March 17, 2008

Cubic numbers

Create a triangle from the sequence of odd numbers s[n]=2n-1 by writing s[1] on the first row, s[2] and s[3] on the second row, the next three numbers from the sequence on the third row, ... the next k numbers on the k-th row. For example:

The vertical column contains the sums by row of the numbers in the triangle. It is easy to see that this column contains the cubic numbers.

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)