## Tuesday, 26 February 2013

### TUESDAY, 26 FEBRURAY 2013

Today is the $57^{th}$ day of the year.

$57 = 3 \times 19$

$57$ is the eighth member of the Tribonacci Numbers, see A000213. Tribonacci Numbers are a natural extension to the Fibonacci Numbers where, instead of the last two numbers being added together, the last three numbers are added together giving a definition of:
$a(n) = a(n - 1) + a(n - 2) + a(n - 3) with a(0) = a(1) = a(2) = 1$
This gives a sequence whose first seventeen numbers are:
$1, 1, 1, 3, 5, 9, 17, 31, 57, 105, 193, 355, 653, 1201, 2209, 4063, 7473$
As you will observe, this sequence gets large very quickly.