Here we have all Euler or alternating sums of a given weight but only up to depth 3.
The basis elements are characterized by that they are Lyndon words over the negative odd integers.
The log files of the runs are
| hex3-7.log.bz2 | Weight 7, (2907) |
| hex3-8.log.bz2 | Weight 8, (4545) |
| hex3-9.log.bz2 | Weight 9, (7748) |
| hex3-10.log.bz2 | Weight 10, (12343) |
| hex3-11.log.bz2 | Weight 11, (30608) |
| hex3-12.log.bz2 | Weight 12, (28444) |
| hex3-13.log.bz2 | Weight 13, (95768) |
| hex3-14.log.bz2 | Weight 14, (64416) |
| hex3-15.log.bz2 | Weight 15, (264842) |
| hex3-16.log.bz2 | Weight 16, (136843) |
| hex3-17.log.bz2 | Weight 17, (852928) |
| hex3-18.log.bz2 | Weight 18, (271840) |
| hex3-19.log.bz2 | Weight 19, (2119420) |
| hex3-20.log.bz2 | Weight 20, (526732) |
| hex3-21.log.bz2 | Weight 21, (4589073) |
| hex3-22.log.bz2 | Weight 22, (941175) |
| hex3-23.log.bz2 | Weight 23, (9240925) |
| hex3-24.log.bz2 | Weight 24, (1599709) |
| hex3-25.log.bz2 | Weight 25, (18104981) |
| hex3-26.log.bz2 | Weight 26, (2704610) |
| hex3-27.log.bz2 | Weight 27, (33151681) |
| hex3-28.log.bz2 | Weight 28, (4315944) |
| hex3-29.log.bz2 | Weight 29, (60543073) |
The .prc files contain the corresponding tables.
| alt7r3.prc.bz2 | Weight 7, (2374) |
| alt8r3.prc.bz2 | Weight 8, (3959) |
| alt9r3.prc.bz2 | Weight 9, (7140) |
| alt10r3.prc.bz2 | Weight 10, (11758) |
| alt11r3.prc.bz2 | Weight 11, (29926) |
| alt12r3.prc.bz2 | Weight 12, (27786) |
| alt13r3.prc.bz2 | Weight 13, (95037) |
| alt14r3.prc.bz2 | Weight 14, (63713) |
| alt15r3.prc.bz2 | Weight 15, (263665) |
| alt16r3.prc.bz2 | Weight 16, (136075) |
| alt17r3.prc.bz2 | Weight 17, (852773) |
| alt18r3.prc.bz2 | Weight 18, (269999) |
| alt19r3.prc.bz2 | Weight 19, (2106830) |
| alt20r3.prc.bz2 | Weight 20, (523244) |
| alt21r3.prc.bz2 | Weight 21, (4571846) |
| alt22r3.prc.bz2 | Weight 22, (935440) |
| alt23r3.prc.bz2 | Weight 23, (9225520) |
| alt24r3.prc.bz2 | Weight 24, (1596878) |
| alt25r3.prc.bz2 | Weight 25, (18033449) |
| alt26r3.prc.bz2 | Weight 26, (2702054) |
| alt27r3.prc.bz2 | Weight 27, (33058066) |
| alt28r3.prc.bz2 | Weight 28, (4303066) |
| alt29r3.prc.bz2 | Weight 29, (60375465) |
The full binary files in FORM format were made with the program tosav.frm and are given by
| alt7r3.sav.bz2 | Weight 7, (2724) |
| alt8r3.sav.bz2 | Weight 8, (4391) |
| alt9r3.sav.bz2 | Weight 9, (7489) |
| alt10r3.sav.bz2 | Weight 10, (12126) |
| alt11r3.sav.bz2 | Weight 11, (29321) |
| alt12r3.sav.bz2 | Weight 12, (27629) |
| alt13r3.sav.bz2 | Weight 13, (87842) |
| alt14r3.sav.bz2 | Weight 14, (61998) |
| alt15r3.sav.bz2 | Weight 15, (224283) |
| alt16r3.sav.bz2 | Weight 16, (127742) |
| alt17r3.sav.bz2 | Weight 17, (712262) |
| alt18r3.sav.bz2 | Weight 18, (256774) |
| alt19r3.sav.bz2 | Weight 19, (1762794) |
| alt20r3.sav.bz2 | Weight 20, (494821) |
| alt21r3.sav.bz2 | Weight 21, (3847595) |
| alt22r3.sav.bz2 | Weight 22, (881715) |
| alt23r3.sav.bz2 | Weight 23, (7794496) |
| alt24r3.sav.bz2 | Weight 24, (1492024) |
| alt25r3.sav.bz2 | Weight 25, (15228167) |
| alt26r3.sav.bz2 | Weight 26, (2452034) |
| alt27r3.sav.bz2 | Weight 27, (27685551) |
| alt28r3.sav.bz2 | Weight 28, (3846605) |
| alt29r3.sav.bz2 | Weight 29, (50906946) |
For advanced use one can use the tablebase facilities of FORM. The .tbl files are
| alt7r3.tbl.bz2 | Weight 7, (2976) |
| alt8r3.tbl.bz2 | Weight 8, (4732) |
| alt9r3.tbl.bz2 | Weight 9, (8014) |
| alt10r3.tbl.bz2 | Weight 10, (12673) |
| alt11r3.tbl.bz2 | Weight 11, (30747) |
| alt12r3.tbl.bz2 | Weight 12, (28258) |
| alt13r3.tbl.bz2 | Weight 13, (93021) |
| alt14r3.tbl.bz2 | Weight 14, (62737) |
| alt15r3.tbl.bz2 | Weight 15, (258724) |
| alt16r3.tbl.bz2 | Weight 16, (131359) |
| alt17r3.tbl.bz2 | Weight 17, (787526) |
| alt18r3.tbl.bz2 | Weight 18, (257913) |
| alt19r3.tbl.bz2 | Weight 19, (1956228) |
| alt20r3.tbl.bz2 | Weight 20, (502243) |
| alt21r3.tbl.bz2 | Weight 21, (4306153) |
| alt22r3.tbl.bz2 | Weight 22, (900594) |
| alt23r3.tbl.bz2 | Weight 23, (8862365) |
| alt24r3.tbl.bz2 | Weight 24, (1541720) |
| alt25r3.tbl.bz2 | Weight 25, (17299258) |
| alt26r3.tbl.bz2 | Weight 26, (2574362) |
| alt27r3.tbl.bz2 | Weight 27, (31577148) |
| alt28r3.tbl.bz2 | Weight 28, (4069613) |
| alt29r3.tbl.bz2 | Weight 29, (58244851) |
The programs we used were:
| hex3.frm | Program to generate these tables, (7788) |
| hex3.h | Library for hex3.frm, (148407) |
| tosav.frm | Program converts htable files to .sav files, (763) |
| maketable.frm | Program converts .prc files to .tbl files, (338) |
| mktbl | Script to run maketable.frm on all files, (1010) |