Answer 2
If you use the above triangle, then you get the sequence b1=1,b2=1,b3=2+1=3,b4=2+2=4,b5=3+4+1=8,b6=3+6+3=12,b7=4+9+7+1=21,....
In this way we get the sequence {1, 1, 3, 4, 8, 12, 21, ...}.
Here we colored the numbers to show how numbers on diagonals add to a sequence.
We can call this sequence a Fibonacci like sequence.
The above sequence satisfies the following equation.
f(1)= 1, f(2)=1 and f(n)=f(n-1)+f(n-2)+ .
We can generalize this sequence, and there are very interesting relations between these Fibonacci like sequences and the well known Fibonacci sequence.
