一道趣题

iseemu2009

不复杂的数列题

王守恩

{1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781},
{3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, 212, 233, 255, 278, 302, 327, 353, 380, 408, 437, 467, 498, 530, 563, 597, 632, 668, 705, 743, 782, 822},
{6, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81, 94, 108, 123, 139, 156, 174, 193, 213, 234, 256, 279, 303, 328, 354, 381, 409, 438, 468, 499, 531, 564, 598, 633, 669, 706, 744, 783, 823, 864},
{10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214, 235, 257, 280, 304, 329, 355, 382, 410, 439, 469, 500, 532, 565, 599, 634, 670, 707, 745, 784, 824, 865, 907},
{15, 20, 26, 33, 41, 50, 60, 71, 83, 96, 110, 125, 141, 158, 176, 195, 215, 236, 258, 281, 305, 330, 356, 383, 411, 440, 470, 501, 533, 566, 600, 635, 671, 708, 746, 785, 825, 866, 908, 951},
{21, 27, 34, 42, 51, 61, 72, 84, 97, 111, 126, 142, 159, 177, 196, 216, 237, 259, 282, 306, 331, 357, 384, 412, 441, 471, 502, 534, 567, 601, 636, 672, 709, 747, 786, 826, 867, 909, 952, 996},
{28, 35, 43, 52, 62, 73, 85, 98, 112, 127, 143, 160, 178, 197, 217, 238, 260, 283, 307, 332, 358, 385, 413, 442, 472, 503, 535, 568, 602, 637, 673, 710, 748, 787, 827, 868, 910, 953, 997, 1042},
{36, 44, 53, 63, 74, 86, 99, 113, 128, 144, 161, 179, 198, 218, 239, 261, 284, 308, 333, 359, 386, 414, 443, 473, 504, 536, 569, 603, 638, 674, 711, 749, 788, 828, 869, 911, 954, 998, 1043, 1089},
{45, 54, 64, 75, 87, 100, 114, 129, 145, 162, 180, 199, 219, 240, 262, 285, 309, 334, 360, 387, 415, 444, 474, 505, 537, 570, 604, 639, 675, 712, 750, 789, 829, 870, 912, 955, 999, 1044, 1090, 1137}

Table[((m + n)^2 - m - 3 n + 2)/2, {m, 9}, {n, 40}]

把对角线取出来——1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, 761, 841, 925, 1013, 1105, 1201, 1301, 1405, 1513, 1625, 1741, 1861, 1985, 2113——A380280——Jan 19 2025。

nyy

如果楼上的通项公式是正确的话，
那么123456789在
第15461行253列

nyy

nyy 发表于 2025-5-14 15:33
如果楼上的通项公式是正确的话，
那么123456789在
第15461行253列

先算出在第多少/，先算出第一行的元素，
在第15713这一斜列，然后平移！

王守恩

接2楼。

第m行,第n列上的数字。$\frac{(m + n)^2 - m - 3 n + 2}{2}$

第666行,第777列上的数字。$\frac{(666 + 777)^2 - 666- 3\cdot777 + 2}{2}=1039627$

对角线。$第m行,第m列上的数字=m^2+(m-1)^2$

数字123456789在m行,n列。$123456789=\frac{(m + n)^2 - m - 3 n + 2}{2}\Rightarrowm=15461, n=253$