Deebie is pretty much correct, it is cylindropuntia ramosissima var. nudum (as in [mostly] spineless) and AFAIK it is called the 'Diamond Cholla', following the pattern on the stems. Indeed the name 'Pencil Cholla' is usually reserved for C. kleiniae.
I have this growing in my yard and the plant came from the Phoenix Desert Botanical Garden. It occurs in the wild in southern Arizona and presumably across the border in Mexico. Is extremely drought tolerant and has really pretty flowers as apparent from the picture in the OP. The spined version is does really cool things with the light if it catches low angle sun... when I get home I will try and find the picture and post it to demonstrate that...
