Tetranacci Numbers Day - August 15

Happy Tetranacci Numbers Day!

You may have heard of the Fibonacci numbers, which starts with 0 and 1, and where every following number is the sum of the previous 2 numbers. Thus Fibonacci numbers are 0, 1, 0+1 = 1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, ...

Mathematicians quickly noticed that they could define a variety of similar sets of numbers by changing the rules slightly. One variation are the Tetranacci numbers (named by merging the tetra- suffix with much of the original Fibonacci name). The Tetranacci numbers start with the "seed numbers" of 0, 1, 1, and 1, and each of the following numbers are the sum of the previous 3 numbers. Thus we get numbers of 0, 0, 0, 1, 0+0+0+1=1, 0+0+1+1=2, 0+1+1+2=4, 1+1+2+4=8, 1+2+4+8=16, ...

While the Fibonacci numbers are known to show up in nature, the Tetranacci numbers are mostly of interest to mathematicians alone. We celebrate Tetranacci numbers on 8/15 because those are the largest sequential Tetranacci numbers that represent a (Gregorian calendar) date.