A036558 Squared distances that can arise in any Barlow packing of spheres of diameter sqrt(3) (the scale being the simplest one that makes this an integer sequence).

0, 3, 6, 8, 9, 11, 12, 15, 17, 18, 19, 20, 21, 22, 24, 25, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86