Challenge: sum of squares. Let's break 299

[Allen]

solution for 400
(the time stamps for my postings are how long it took my 7-year-old computer to calculate each one)

len 400:(383, 346, 330, 295, 381, 348, 328, 297, 379, 350, 326, 299, 377, 352, 324, 301, 375, 354, 271, 258, 367, 362, 314, 311, 365, 364, 312, 264, 361, 368, 257, 319, 357, 372, 304, 272, 353, 376, 300, 325, 351, 378, 298, 327, 349, 380, 296, 329, 347, 382, 294, 331, 345, 384, 400, 225, 259, 366, 363, 262, 267, 309, 316, 260, 269, 307, 318, 358, 371, 305, 320, 356, 373, 303, 273, 256, 369, 360, 216, 268, 308, 317, 359, 370, 306, 270, 355, 374, 302, 227, 398, 386, 290, 335, 394, 390, 339, 337, 392, 284, 341, 388, 396, 333, 343, 233, 128, 313, 263, 266, 310, 174, 226, 399, 385, 291, 334, 242, 287, 338, 391, 393, 336, 289, 387, 397, 332, 293, 236, 340, 389, 395, 230, 254, 275, 209, 232, 344, 281, 203, 197, 244, 240, 201, 283, 342, 234, 250, 279, 162, 322, 207, 277, 252, 148, 176, 265, 219, 222, 139, 261, 315, 169, 231, 210, 274, 255, 321, 208, 276, 253, 323, 206, 235, 249, 192, 292, 237, 247, 282, 202, 239, 245, 196, 288, 241, 200, 161, 280, 204, 157, 243, 286, 198, 126, 163, 278, 251, 190, 171, 229, 212, 149, 175, 186, 214, 147, 177, 223, 218, 182, 179, 221, 220, 180, 144, 217, 224, 137, 187, 213, 228, 172, 152, 248, 193, 168, 156, 205, 195, 166, 123, 238, 246, 154, 170, 191, 98, 127, 129, 160, 164, 125, 199, 285, 115, 141, 183, 178, 146, 215, 185, 104, 121, 135, 189, 211, 113, 83, 173, 188, 101, 155, 134, 122, 167, 194, 130, 159, 165, 124, 132, 93, 103, 153, 72, 184, 140, 116, 109, 87, 138, 151, 105, 120, 136, 89, 80, 145, 111, 114, 82, 143, 181, 108, 88, 81, 63, 106, 150, 75, 94, 102, 67, 158, 131, 65, 79, 117, 52, 69, 100, 96, 73, 71, 50, 119, 77, 92, 133, 36, 64, 57, 112, 84, 85, 59, 62, 107, 118, 78, 91, 53, 47, 97, 99, 70, 74, 95, 49, 32, 68, 76, 45, 55, 66, 34, 110, 86, 58, 42, 39, 25, 56, 44, 37, 27, 142, 54, 90, 31, 18, 46, 35, 29, 20, 61, 60, 40, 41, 23, 13, 51, 30, 19, 17, 8, 28, 21, 15, 10, 26, 38, 43, 6, 3, 22, 14, 11, 5, 4, 12, 24, 1, 48, 33, 16, 9, 7, 2)