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## Sunday, April 20, 2008

### Tribonacci numbers

The Tribonacci numbers are defined as

$T_n=T_{n-3}+T_{n-2}+T_{n-1}$

If we set the first three numbers at 0,1 and 1, then the generating function is

$T(x)=\frac{x}{1-x-x^2-x^3}$,

and the first 15 Tribonacci numbers are
0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, ...

Source: MathWorld

The Tribonacci Numbers look a lot like the Fibonacci numbers, that's how they got their name anyway. Who was Fibonacci? Fibonacci, or Leonardo of Pisa (1170-1250) was an Italian mathematician who introduced the arabic numbers ( the numbers we use today ) in Europe in his book Liber Abaci.

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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.)