A)In the Fibonacci sequence, Fibonacci assumed that each rabbit took one month to mature. Now assume that rabbits take four month to mature. The sequence is defined by

g 0 = 1, g 1 = 1, g 2 = 1, g 3 = 1 , g 4 = 1 and for n > 4 g_n = g_n-1 + g_n-5 so g 5 = 2

Write MATLAB code for calculating a Fibonacci-like number with these new conditions. How many pairs of rabbits are there after 12 months (so g₁₂)?

B)

What if rabbits took 2 months to mature, yielding a sequence h. We can derive an estimate

In fact, we propose that maybe

This works for the first few small values of n, and also seems to work fine for large values of n. Determine and c and fill rounded versions of them in here, rounding to 4 decimal places after the decimal point and with a leading zero only if the value is less than 1 (for example, 1.2345 and 0.0012 like would be produced with MATLAB "format short"). Do not use scientific notation unless "format short" would do so. is --------- and c is ------------ .

Hint: Please refer to page 26 of the Moler book.

Can someone implement a function for A in matlab and give resulting Y and C for B) please with explanation. Thank you