Challenge: sum of squares. Let's break 299

[Allen]

Here's a len 999 to prove it does not blow up too much in size as N increases.

len 999:(936, 913, 851, 830, 934, 915, 849, 832, 932, 917, 847, 834, 930, 919, 845, 836, 928, 921, 843, 838, 926, 923, 841, 840, 924, 925, 839, 842, 922, 927, 837, 844, 920, 929, 835, 846, 918, 931, 833, 848, 916, 933, 831, 850, 999, 937, 912, 852, 997, 939, 910, 854, 995, 941, 908, 856, 993, 943, 906, 858, 991, 945, 904, 860, 989, 947, 902, 862, 987, 949, 900, 864, 985, 951, 730, 791, 973, 963, 801, 880, 969, 967, 882, 799, 965, 971, 878, 803, 961, 975, 874, 890, 959, 977, 872, 809, 955, 981, 868, 896, 785, 979, 870, 811, 953, 983, 698, 746, 935, 914, 686, 683, 998, 938, 911, 853, 996, 940, 909, 855, 994, 942, 907, 857, 992, 944, 905, 859, 990, 946, 903, 861, 988, 948, 901, 863, 986, 950, 731, 790, 974, 962, 802, 798, 966, 970, 879, 885, 796, 968, 881, 800, 964, 972, 877, 804, 960, 976, 788, 812, 869, 980, 784, 897, 867, 982, 954, 810, 871, 978, 958, 891, 873, 648, 952, 984, 865, 816, 628, 893, 956, 808, 792, 889, 875, 806, 794, 887, 634, 735, 786, 895, 626, 818, 782, 899, 701, 743, 778, 822, 699, 745, 776, 824, 697, 747, 774, 826, 695, 749, 772, 828, 693, 676, 768, 753, 691, 678, 766, 755, 689, 680, 764, 757, 687, 402, 894, 787, 734, 635, 886, 795, 805, 876, 888, 793, 807, 957, 892, 789, 732, 637, 884, 797, 647, 578, 866, 898, 702, 742, 779, 821, 700, 744, 625, 819, 781, 740, 629, 815, 706, 663, 633, 736, 708, 813, 631, 738, 783, 817, 627, 669, 775, 825, 696, 748, 773, 827, 694, 750, 771, 829, 692, 677, 767, 754, 690, 679, 765, 756, 688, 681, 763, 758, 611, 685, 759, 762, 607, 549, 820, 780, 741, 703, 666, 630, 814, 707, 737, 632, 664, 705, 739, 486, 883, 638, 587, 709, 660, 636, 733, 711, 585, 640, 729, 715, 654, 642, 583, 713, 512, 577, 579, 646, 650, 719, 725, 644, 652, 717, 727, 362, 599, 770, 751, 545, 544, 612, 684, 760, 761, 608, 617, 752, 769, 675, 621, 823, 777, 592, 497, 659, 710, 586, 639, 657, 712, 584, 641, 728, 716, 580, 576, 649, 720, 724, 645, 651, 718, 726, 643, 653, 503, 722, 574, 582, 714, 655, 501, 588, 568, 521, 704, 665, 491, 598, 558, 667, 489, 600, 556, 533, 623, 673, 416, 484, 605, 551, 674, 622, 603, 553, 672, 624, 601, 488, 668, 557, 532, 492, 597, 559, 530, 494, 662, 563, 593, 431, 658, 567, 589, 500, 656, 569, 520, 504, 721, 575, 581, 508, 516, 573, 723, 502, 459, 565, 591, 498, 463, 561, 595, 366, 534, 555, 670, 419, 542, 614, 682, 543, 418, 671, 485, 539, 550, 606, 619, 537, 487, 602, 554, 535, 365, 596, 560, 529, 495, 661, 564, 525, 499, 590, 566, 458, 442, 519, 505, 456, 444, 517, 572, 452, 509, 515, 446, 338, 562, 594, 430, 411, 613, 476, 548, 541, 615, 610, 546, 415, 369, 531, 493, 468, 432, 409, 552, 604, 420, 421, 540, 616, 609, 547, 294, 435, 406, 618, 538, 423, 477, 364, 536, 620, 341, 443, 518, 506, 335, 449, 451, 510, 514, 447, 453, 571, 329, 400, 441, 288, 496, 528, 433, 467, 374, 410, 490, 471, 370, 414, 427, 473, 368, 361, 480, 481, 360, 424, 417, 367, 474, 426, 199, 330, 511, 450, 391, 570, 454, 507, 393, 448, 513, 328, 401, 440, 460, 381, 403, 438, 462, 379, 405, 436, 464, 377, 407, 434, 527, 257, 472, 428, 413, 371, 358, 483, 478, 363, 262, 522, 439, 461, 268, 408, 376, 524, 437, 292, 284, 392, 337, 339, 445, 455, 386, 398, 331, 345, 384, 457, 327, 349, 380, 404, 325, 300, 429, 412, 372, 469, 315, 526, 258, 318, 466, 375, 354, 271, 305, 479, 482, 359, 425, 475, 254, 422, 203, 281, 344, 332, 293, 383, 346, 279, 397, 387, 342, 334, 395, 389, 287, 289, 336, 340, 285, 291, 385, 399, 277, 299, 326, 350, 275, 301, 324, 352, 273, 211, 465, 264, 265, 311, 314, 470, 259, 270, 355, 321, 304, 225, 351, 378, 298, 278, 347, 382, 243, 333, 396, 280, 296, 233, 343, 282, 394, 390, 235, 206, 523, 261, 223, 353, 323, 302, 274, 210, 319, 357, 219, 310, 266, 263, 313, 312, 217, 267, 309, 316, 260, 269, 356, 373, 252, 189, 295, 234, 207, 322, 303, 181, 348, 228, 256, 320, 209, 232, 297, 144, 180, 220, 221, 308, 317, 212, 272, 169, 231, 253, 276, 208, 192, 249, 151, 290, 286, 198, 202, 239, 245, 196, 204, 237, 388, 188, 173, 227, 214, 147, 177, 307, 222, 178, 306, 135, 154, 246, 283, 201, 240, 244, 156, 205, 236, 248, 193, 131, 230, 170, 191, 250, 150, 174, 226, 215, 146, 143, 218, 182, 179, 145, 255, 229, 132, 124, 200, 241, 159, 130, 194, 247, 153, 171, 190, 251, 149, 140, 184, 216, 108, 117, 172, 152, 137, 224, 176, 148, 213, 187, 102, 123, 238, 162, 127, 197, 164, 160, 129, 195, 166, 158, 242, 119, 106, 183, 141, 115, 110, 86, 139, 185, 104, 121, 168, 88, 81, 175, 186, 103, 122, 134, 155, 101, 68, 128, 161, 163, 126, 99, 157, 167, 58, 111, 85, 84, 112, 113, 83, 142, 114, 82, 62, 107, 118, 138, 87, 109, 116, 80, 89, 136, 120, 105, 91, 165, 31, 69, 75, 94, 50, 71, 73, 96, 100, 125, 44, 56, 65, 79, 90, 54, 67, 77, 92, 133, 36, 64, 57, 43, 78, 66, 55, 45, 76, 93, 51, 70, 74, 95, 49, 72, 97, 47, 53, 28, 21, 60, 61, 39, 42, 22, 27, 37, 63, 18, 46, 98, 23, 41, 59, 5, 20, 29, 52, 48, 33, 16, 9, 40, 24, 25, 11, 38, 26, 10, 15, 34, 30, 19, 6, 3, 13, 12, 4, 32, 17, 8, 1, 35, 14, 2, 7)