make a checkerboard from an appropriately-sized table

checkerboard.sql

-- By using a table with 4^zoom rows, the following sql statement produces a checkboard
-- The following config works for making a checkerboard with zoom = 3 (4^3 = 64 rows)
WITH
  vars AS (SELECT 3 AS zoom)

SELECT 
  (8 * ss.c1 + ss.c2 = ss.cartodb_id) as tf,
  ss.c1,
  ss.c2,
  ss.cartodb_id as cartodb_id,
  CASE 
    WHEN
      ss.cartodb_id % 2 = 0 AND ss.c1 % 2 = 0
    THEN 
        CDB_XYZ_Extent(c1,c2,vars.zoom)
    WHEN
      ss.cartodb_id % 2 = 1 AND ss.c1 % 2 = 1
    THEN
        CDB_XYZ_Extent(c1,c2,vars.zoom)
    ELSE 
      null 
    END AS the_geom_webmercator
FROM (
  SELECT 
    floor((cartodb_id-1) / (1 << vars.zoom))::int as c1,
    (cartodb_id % (1 << vars.zoom))::int as c2,
    cartodb_id
  from for_loops, vars) as ss, vars
ORDER BY c1, c2