Answer: Unfortunately, the conditions you are describing would be very difficult for most plants to tolerate in combination. The only plants I can think of that might meet all the conditions are Mazus repens and golden creeping jenny or Lysimachia nummularia aurea. Since I have not seen either one listed as being walnut-tolerant or intolerant, I would have to suggest you experiment with a few plants and see how they do before planting the entire area.
Another approach might be to place the pavers flush together and plant the perimeter with plants such as hostas, liriope, or periwinkle (Vinca minor) to soften the overall effect. You could perhaps add some large containers of shade tolerant annuals such as caladiums and impatiens for summer color.
Good luck with your project!
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