An -pyramid is created with blocks at the base, − 1 blocks on the next level, until the peak which has 1 block.

Pyramids are colored according to the following rules: (1) Each block can be red, gold, or black, and (2) All 3-block units composed of one block on top of two others must either all be the same color or all be different colors. Answer the following:

a) How many ways are there to color a 7-pyramid?

b) What is the maximum number of black blocks in a 25-pyramid that has at least one red block and at least one gold block?