A036559 Squared distances that cannot arise in any Barlow packing of spheres of diameter sqrt(3) (the scale being the simplest one that makes this an integer sequence).

1, 2, 4, 5, 7, 10, 13, 14, 16, 23, 26, 28, 38, 40, 42, 52, 58, 64, 74, 90, 104, 106, 112, 122, 138, 154, 160, 168, 170, 186, 202, 208, 218, 230, 232, 234, 250, 256, 266, 282, 296, 298, 314, 330, 346, 360, 362, 378, 394, 410, 416, 424, 426, 442, 448