MathDB

Rosemonde is stacking spheres to make pyramids. She constructs two types of pyramids

S_n

and

T_n

. The pyramid

S_n

has

n

layers, where the top layer is a single sphere and the

i^{th}

layer is an

i\times

i square grid of spheres for each

2 \le i \le n

. Similarly, the pyramid

T_n

has

n

layers where the top layer is a single sphere and the

i^{th}

layer is

\frac{i(i+1)}{2}

spheres arranged into an equilateral triangle for each

2 \le i \le n

Problem Statement