L=0~32 ; H=0~23 八邊形圖框的面積 Area=L^2+4LH+2H^2
H*SQRT(2) | H\L | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |
0 | 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 | 121 | 144 | 169 | 196 | 225 | 256 | 289 | 324 | 361 | 400 | 441 | 484 | 529 | 576 | 625 | 676 | 729 | 784 | 841 | 900 | 961 | 1024 | ||
1.414 | 1 | 2 | 7 | 14 | 23 | 34 | 47 | 62 | 79 | 98 | 119 | 142 | 167 | 194 | 223 | 254 | 287 | 322 | 359 | 398 | 439 | 482 | 527 | 574 | 623 | 674 | 727 | 782 | 839 | 898 | 959 | 1022 | 1087 | 1154 |
2.828 | 2 | 8 | 17 | 28 | 41 | 56 | 73 | 92 | 113 | 136 | 161 | 188 | 217 | 248 | 281 | 316 | 353 | 392 | 433 | 476 | 521 | 568 | 617 | 668 | 721 | 776 | 833 | 892 | 953 | 1016 | 1081 | 1148 | 1217 | 1288 |
4.243 | 3 | 18 | 31 | 46 | 63 | 82 | 103 | 126 | 151 | 178 | 207 | 238 | 271 | 306 | 343 | 382 | 423 | 466 | 511 | 558 | 607 | 658 | 711 | 766 | 823 | 882 | 943 | 1006 | 1071 | 1138 | 1207 | 1278 | 1351 | 1426 |
5.657 | 4 | 32 | 49 | 68 | 89 | 112 | 137 | 164 | 193 | 224 | 257 | 292 | 329 | 368 | 409 | 452 | 497 | 544 | 593 | 644 | 697 | 752 | 809 | 868 | 929 | 992 | 1057 | 1124 | 1193 | 1264 | 1337 | 1412 | 1489 | 1568 |
7.071 | 5 | 50 | 71 | 94 | 119 | 146 | 175 | 206 | 239 | 274 | 311 | 350 | 391 | 434 | 479 | 526 | 575 | 626 | 679 | 734 | 791 | 850 | 911 | 974 | 1039 | 1106 | 1175 | 1246 | 1319 | 1394 | 1471 | 1550 | 1631 | 1714 |
8.485 | 6 | 72 | 97 | 124 | 153 | 184 | 217 | 252 | 289 | 328 | 369 | 412 | 457 | 504 | 553 | 604 | 657 | 712 | 769 | 828 | 889 | 952 | 1017 | 1084 | 1153 | 1224 | 1297 | 1372 | 1449 | 1528 | 1609 | 1692 | 1777 | 1864 |
9.899 | 7 | 98 | 127 | 158 | 191 | 226 | 263 | 302 | 343 | 386 | 431 | 478 | 527 | 578 | 631 | 686 | 743 | 802 | 863 | 926 | 991 | 1058 | 1127 | 1198 | 1271 | 1346 | 1423 | 1502 | 1583 | 1666 | 1751 | 1838 | 1927 | 2018 |
11.314 | 8 | 128 | 161 | 196 | 233 | 272 | 313 | 356 | 401 | 448 | 497 | 548 | 601 | 656 | 713 | 772 | 833 | 896 | 961 | 1028 | 1097 | 1168 | 1241 | 1316 | 1393 | 1472 | 1553 | 1636 | 1721 | 1808 | 1897 | 1988 | 2081 | 2176 |
12.728 | 9 | 162 | 199 | 238 | 279 | 322 | 367 | 414 | 463 | 514 | 567 | 622 | 679 | 738 | 799 | 862 | 927 | 994 | 1063 | 1134 | 1207 | 1282 | 1359 | 1438 | 1519 | 1602 | 1687 | 1774 | 1863 | 1954 | 2047 | 2142 | 2239 | 2338 |
14.142 | 10 | 200 | 241 | 284 | 329 | 376 | 425 | 476 | 529 | 584 | 641 | 700 | 761 | 824 | 889 | 956 | 1025 | 1096 | 1169 | 1244 | 1321 | 1400 | 1481 | 1564 | 1649 | 1736 | 1825 | 1916 | 2009 | 2104 | 2201 | 2300 | 2401 | 2504 |
15.556 | 11 | 242 | 287 | 334 | 383 | 434 | 487 | 542 | 599 | 658 | 719 | 782 | 847 | 914 | 983 | 1054 | 1127 | 1202 | 1279 | 1358 | 1439 | 1522 | 1607 | 1694 | 1783 | 1874 | 1967 | 2062 | 2159 | 2258 | 2359 | 2462 | 2567 | 2674 |
16.970 | 12 | 288 | 337 | 388 | 441 | 496 | 553 | 612 | 673 | 736 | 801 | 868 | 937 | 1008 | 1081 | 1156 | 1233 | 1312 | 1393 | 1476 | 1561 | 1648 | 1737 | 1828 | 1921 | 2016 | 2113 | 2212 | 2313 | 2416 | 2521 | 2628 | 2737 | 2848 |
18.385 | 13 | 338 | 391 | 446 | 503 | 562 | 623 | 686 | 751 | 818 | 887 | 958 | 1031 | 1106 | 1183 | 1262 | 1343 | 1426 | 1511 | 1589 | 1687 | 1778 | 1871 | 1966 | 2063 | 2162 | 2263 | 2366 | 2471 | 2578 | 2687 | 2798 | 2911 | 3026 |
19.799 | 14 | 392 | 449 | 508 | 569 | 632 | 697 | 764 | 833 | 904 | 977 | 1052 | 1129 | 1208 | 1289 | 1372 | 1457 | 1544 | 1633 | 1724 | 1817 | 1912 | 2009 | 2108 | 2209 | 2312 | 2417 | 2524 | 2633 | 2744 | 2857 | 2972 | 3089 | 3208 |
21.213 | 15 | 450 | 511 | 574 | 639 | 706 | 775 | 846 | 919 | 994 | 1071 | 1150 | 1231 | 1314 | 1399 | 1486 | 1575 | 1666 | 1759 | 1854 | 1951 | 2050 | 2151 | 2254 | 2359 | 2466 | 2575 | 2686 | 2799 | 2914 | 3031 | 3150 | 3271 | 3394 |
22.627 | 16 | 512 | 577 | 644 | 713 | 784 | 857 | 932 | 1009 | 1088 | 1169 | 1252 | 1337 | 1424 | 1513 | 1604 | 1697 | 1792 | 1889 | 1988 | 2089 | 2192 | 2297 | 2404 | 2513 | 2624 | 2737 | 2852 | 2969 | 3088 | 3209 | 3332 | 3457 | 3584 |
24.042 | 17 | 578 | 647 | 718 | 791 | 866 | 943 | 1022 | 1103 | 1186 | 1271 | 1358 | 1447 | 1538 | 1631 | 1726 | 1823 | 1922 | 2023 | 2126 | 2231 | 2338 | 2447 | 2558 | 2671 | 2786 | 2903 | 3022 | 3143 | 3266 | 3391 | 3518 | 3647 | 3778 |
25.456 | 18 | 648 | 721 | 796 | 873 | 952 | 1033 | 1116 | 1201 | 1288 | 1377 | 1468 | 1561 | 1656 | 1753 | 1852 | 1953 | 2056 | 2161 | 2268 | 2377 | 2488 | 2601 | 2716 | 2833 | 2952 | 3073 | 3196 | 3321 | 3448 | 3577 | 3708 | 3841 | 3976 |
26.870 | 19 | 722 | 799 | 878 | 959 | 1042 | 1127 | 1214 | 1303 | 1394 | 1487 | 1582 | 1679 | 1778 | 1879 | 1982 | 2087 | 2194 | 2303 | 2414 | 2527 | 2642 | 2759 | 2878 | 2999 | 3122 | 3247 | 3374 | 3503 | 3634 | 3767 | 3902 | 4039 | 4178 |
28.284 | 20 | 800 | 881 | 964 | 1049 | 1136 | 1225 | 1316 | 1409 | 1504 | 1601 | 1700 | 1801 | 1904 | 2009 | 2116 | 2225 | 2336 | 2449 | 2564 | 2681 | 2800 | 2921 | 3044 | 3169 | 3296 | 3425 | 3556 | 3689 | 3824 | 3961 | 4100 | 4241 | 4384 |
29.698 | 21 | 882 | 967 | 1054 | 1143 | 1234 | 1327 | 1422 | 1519 | 1618 | 1719 | 1822 | 1927 | 2034 | 2143 | 2254 | 2367 | 2482 | 2599 | 2718 | 2839 | 2962 | 3087 | 3214 | 3343 | 3474 | 3607 | 3742 | 3879 | 4018 | 4159 | 4302 | 4447 | 4594 |
31.113 | 22 | 968 | 1057 | 1148 | 1241 | 1336 | 1433 | 1532 | 1633 | 1736 | 1841 | 1948 | 2057 | 2168 | 2281 | 2396 | 2513 | 2632 | 2753 | 2876 | 3001 | 3128 | 3257 | 3388 | 3521 | 3656 | 3793 | 3932 | 4073 | 4216 | 4361 | 4508 | 4657 | 4808 |
32.527 | 23 | 1058 | 1151 | 1246 | 1343 | 1442 | 1543 | 1646 | 1751 | 1858 | 1967 | 2078 | 2191 | 2306 | 2423 | 2542 | 2663 | 2786 | 2911 | 3038 | 3167 | 3298 | 3431 | 3566 | 3703 | 3842 | 3983 | 4126 | 4271 | 4418 | 4567 | 4718 | 4871 | 5026 |
多半方塊 ( Polytans or Polyaboloes ) 型片數及覆蓋面積表
N-tan | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
No. of Pieces | 1 | 3 | 4 | 14 | 30 | 107 | 318 | 1116 | 3743 | 13240 |
Area (N) | 0.5 | 3 | 6 | 28 | 75 | 321 | 1113 | 4464 | 16843.5 | 66200 |
Area ((N-1)+N) | 3.5 | 9 | 34 | 103 | 396 | 1434 | 5577 | 21307.5 | 83043.5 | |
Area ((N-2)+(N-1)+N) | 9.5 | 37 | 109 | 424 | 1509 | 5898 | 22420.5 | 87507.5 |
See also On-Line Encyclopedia of Integer Sequences by N.J.A. Sloane , ID Number: A006074
單面 ( One-Sided ) 多半方塊型片數及覆蓋面積表
One-Sided N-tan | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
No. of Pieces | 1 | 4 | 6 | 22 | 56 | 198 | 624 |
Area (N) | 0.5 | 4 | 9 | 44 | 140 | 594 | 2184 |
Area ((N-1)+N) | 4.5 | 13 | 53 | 184 | 734 | 2778 | |
Area ((N-2)+(N-1)+N) | 13.5 | 57 | 193 | 778 | 2918 |