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Consider the recurrence ti+2 = 6ti+1 - 8ti, for t0 = 0 and t1 = 1....

Consider the recurrence ti+2 = 6ti+1 - 8ti, for t0 = 0 and t1 = 1. For what values of i is ti of the form k(k + 1)/2 for some integer k? Show all work.

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Answer #1

Please don't forget to give me thumbs up for my hard work and trying to solve your problem

Thanks in Advance

If you still have any problem comment me I will reply

 def function_t(n): if n ==0: return 0 elif n==1: return 1 else: return 6*function_t(n-1) -8*function_t(n-2) all=[] for i in range(40): all.append(function_t(i)) for i in range(10000000): k=i*(i+1)/2 if k in all: print(all.index(k))

I did coding in Google Collaboratory(Python)

and final output shows all values of ti are of form k(k+1)/2  

Hope this code helps you and please give me thumbs up that really matters

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