# The Two who Reccur

Discrete Mathematics Level 4

Let there be two sequences defined as

{$$a_n$$} =$$\large \sum_{j=1}^n \sum_{k=j}^n \dbinom n k \dbinom k j$$

and {$$b_n$$} = {$$a_n$$} +$$2^{n+1}$$

Then {$$b_{n+1}$$} can be given by the following recurrence formula

{$$b_{n+1}$$} = $$\alpha$$ {$$b_n$$} + $$\beta$$ {$$b_{n-1}$$} where $$\alpha$$ and $$\beta$$ are constant integers. Find $$\alpha$$ + $$\beta$$

Hint: {$$a_{n+1}$$} can also be given by the same recurrence formula

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