# How quickly can you do this?

Let $$a$$ be the number of tuples $$(a_1,a_2,a_3,\ldots)$$ that satisfy the equation given below : $\sum_{i=1}^{\infty} ia_{i}=45$

Let $$b$$ be the number of tuples $$(b_1,b_2,b_3,\ldots)$$ that satisfy the inequality given below : $\sum_{i=1}^{\infty} (i+1)b_{i}\leq 45$

Enter your answer by concatenating $$a$$ and $$b$$. For example, if $$a=23$$ and $$b=65$$, then enter $$2365$$ as your answer.

Details and Assumptions

• $$a_{i}\geq 0\ \forall\ i\in \Bbb Z^{+}$$
• $$b_{i}\geq 0\ \forall\ i\in \Bbb Z^{+}$$
• $$\Bbb Z^{+}$$ denotes the set of all positive integers.
• By title, I mean how quickly your program can do this.

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