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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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