Suppose $W_{1} = 1$, $W_{2} = 2$ and for $n > 2$, $W_{n} = W_{1} + W_{2} + \dots + W_{n-2} + 2$.
Find the values of $W_{1}, W_{2}, \dots, W_{8}$. Do you recognise this sequence?

$W_1 = 1$

$W_2 = 2$

$W_3 = W_1 + 2 = 1 + 2 = 3$

$W_4 = W_1 + W_2 + 2 = 1 + 2 + 2 = 5$

$W_5 = W_1 + W_2 + W_3 + 2 = 1 + 2 + 3 + 2 = 8$

$W_6 = W_1 + W_2 + W_3 + W_4 + 2$

$= 1 + 2 + 3 + 5 + 2 = 13$

$W_7 = 1 + 2 + 3 + 5 + 8 + 2 = 21$

$W_8 = 1 + 2 + 3 + 5 + 8 + 13 + 2 = 34$

The sequence 1, 2, 3, 5, 8, 13, 21, 34, ... is the Virahānka–Fibonacci sequence.