I was able to get an n = 300 "square" necklace using Kocay's program. For the skeptical here it is: 1, 288, 112, 212, 188, 136, 153, 103, 186, 138, 151, 74, 122, 134, 190, 99, 157, 167, 194, 206, 118, 171, 54, 142, 83, 113, 56, 140, 184, 105, 219, 181, 108, 148, 77, 179, 110, 146, 50, 119, 170, 191, 133, 156, 100, 125, 164, 197, 59, 137, 187, 102, 154, 135, 121, 75, 150, 106, 183, 73, 152, 104, 185, 139, 222, 178, 78, 147, 214, 227, 173, 116, 208, 81, 144, 180, 109, 215, 226, 174, 115, 209, 80, 176, 224, 217, 72, 289, 35, 221, 220, 69, 292, 32, 257, 67, 294, 30, 259, 65, 296, 28, 261, 63, 298, 26, 263, 61, 300, 24, 265, 264, 25, 299, 62, 262, 27, 297, 64, 260, 29, 295, 66, 258, 31, 293, 68, 256, 33, 291, 70, 254, 2, 287, 37, 252, 4, 285, 39, 250, 6, 283, 41, 248, 8, 281, 43, 246, 10, 279, 45, 244, 12, 277, 47, 242, 14, 275, 49, 240, 16, 273, 88, 236, 20, 269, 92, 232, 168, 57, 199, 162, 127, 98, 158, 131, 193, 96, 228, 172, 53, 203, 86, 238, 18, 271, 90, 234, 22, 267, 94, 230, 211, 189, 36, 160, 129, 195, 166, 123, 201, 55, 141, 84, 205, 51, 145, 216, 225, 175, 114, 210, 231, 93, 268, 21, 235, 89, 200, 124, 132, 192, 97, 128, 161, 163, 126, 130, 159, 165, 196, 60, 229, 95, 266, 23, 233, 91, 270, 19, 237, 52, 272, 17, 239, 85, 204, 120, 169, 155, 101, 223, 177, 79, 117, 207, 82, 143, 218, 182, 107, 149, 76, 213, 111, 58, 198, 202, 87, 274, 15, 241, 48, 276, 13, 243, 46, 278, 11, 245, 44, 280, 9, 247, 42, 282, 7, 249, 40, 284, 5, 251, 38, 286, 3, 253, 71, 290, 34, 255 ------------------------------------------------------------ W. Edwin Clark, Math Dept, University of South Florida, http://www.math.usf.edu/~eclark/ ------------------------------------------------------------