Software to pixelate an image with alternating offset rows?

[JenniferMurphy]

This is a bit of an odd request. I hope it is appropriate for this section.

I recently purchased a set of building blocks called PinBlocks. Here's there website. I have no other connection with the company whatsoever.

Pinblock Building Toy

One of the cool things about these blocks is that they are small enough (1.0 cm square) that they can be used to construct pixelated versions of images, such as cartoon characters and even faces. The problem is converting a clip art image of the cartoon character or a photo into a pixelated template for use in constructing the project.

There are two problems:

1. The pixels need to be one of the 20 colors that the blocks come in or, one of the (less than 20) colors of the blocks I have on hand.
   
2. The pixelation cannot be a regular grid, as is usually the case. Each PinBlock has 2 connecting pins, so every other row must be offset by half a block, like a brick wall, or the project will fall apart into separate columns. So every other row of pixels needs to be offset by half a pixel.

IrfanView does a pretty good job of pixelization (what it calls pixelizing), but it does not have a way to limit the colors or to offset every other row.

Is there any software that doesn't cost an arm and a leg that will allow me to create a PinBlock template from a clip art image or a photo?

Let me know if I didn't explain this clearly.