Let g(n) = 2g(n-1) + g(n-2), g(0)=0, g(1)=1.(adsbygoogle = window.adsbygoogle || []).push({});

The explicit formula is g(n) = ((1+t)^n - (1-t)^n) / (2t), where t is sqrt(2).

Let h(n) = the sum of the first n+1 terms of g, ie h(n) = g(0)+g(1)+...+g(n).

Then a possible recursive definition of h(n) will be similar to that of g(n), except that 1 will have to be added to it each time:

h(n) = 2h(n-1) + h(n-2) + 1, h(0)=0, h(1)=1.

How can I find (or what is) the explicit formula for h(n), please?

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# A Fibonacci type sequence

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