Simple Imperfect Squared Rectangles were produced by computer in large quantities by Bouwkamp, Duijvestijn and Medema in the search for Perfect Squares Squares in the early 60's. Like SISS's, they often have interesting semi-symmetrical constructions. This sequence is listed in the OEIS as A002881.

Below are bouwkampcodes of the tilings, the display menus and pdfs to the left. Right click on the bouwkampcode links and select 'save link as ...', to save the files (or similar for your browser)
Simple Imperfect Squared Rectangle, Order 13: 51 x 29