Tetranacci Number

The tetranacci numbers are a generalization of the Fibonacci Numbers defined by $T_0=0$, $T_1=1$, $T_2=1$, $T_3=2$, and the Recurrence Relation

$$T_n=T_{n-1}+T_{n-2}+T_{n-3}+T_{n-4}$$

for $n\geq 4$. They represent the $n=4$ case of the Fibonacci n-Step Number. The first few terms are 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, ... (Sloane's A000078). The ratio of adjacent terms tends to 1.92756, which is the Real Root of $x^5-2x^4+1=0$.

See also Fibonacci n-Step Number, Fibonacci Number, Tribonacci Number

References

Sloane, N. J. A. Sequence A000078/M1108 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.