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Number of royal factions for arities 0...5: 1, 1, 1, 2, 11, 272
This triangle shows the representatives of each royal faction.
0
1
2
3
4
|
[0]
[0]
[0]
[0, 40]
[0, 680, 1632, 2176, 3808, 5760, 6856, 10920, 11464, 26752, 28384]
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| row 5 of length 272: 0, 174760, 419424 ... 2091314912, 2091559592, 2093664936
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[0, 174760, 419424, 559232, 664104, 978656, 1480320, 1603680, 1757896, 2631680, 2785960, 2942152, 3034720, 4112000, 6875264, 7245536, 8289792, 8421376, 8840800, 9085480, 10025056, 10395136, 11053056, 11456096, 16711168, 18245760, 18384480, 18492616, 18800640, 19453440, 19561640, 19837024, 20769320, 23772200, 25067520, 25351336, 25753216, 26667136, 26913992, 27983016, 36208640, 36317864, 36457672, 36628064, 37534760, 37775488, 37929512, 38330368, 38700640, 39081128, 39255552, 39500360, 39640104, 39745152, 40561192, 40668232, 41712808, 41866752, 42107560, 42263752, 42508416, 42911456, 43433600, 43711176, 43818152, 44739240, 44879048, 46196864, 46844584, 47502504, 48166528, 50134184, 54454400, 56159968, 56526976, 57196160, 57596128, 58491560, 58775040, 59158624, 59438120, 60090920, 60337760, 60737536, 61406720, 62702120, 63232584, 63895648, 107129512, 107513984, 107933408, 108435072, 108558432, 108712648, 109109248, 109479520, 109756968, 110279240, 110663776, 111083008, 111340072, 111724544, 112111200, 112242784, 112645632, 113046568, 115795552, 116979808, 125339232, 125755392, 126006440, 126391936, 126808288, 126938848, 127585480, 127975040, 128375008, 128776904, 129164488, 132707968, 142781096, 143165568, 143584992, 143716576, 144086656, 144364232, 144744576, 145147616, 145548488, 145947336, 146331872, 146718336, 149481600, 150402688, 160605256, 161406976, 161674280, 162059776, 162443360, 163375656, 166131808, 178430504, 178570312, 179234400, 179370080, 180017736, 180141096, 180936704, 181861888, 182246440, 183167528, 183825448, 197060736, 198766304, 199555784, 250539744, 250671328, 375941248, 376095272, 377421312, 377662120, 378046592, 378466016, 378967680, 379245256, 380429512, 381599360, 384362624, 394329600, 394696800, 394976296, 396288000, 398256680, 411099136, 411469408, 411746856, 412269128, 412653664, 413072896, 413329960, 413714432, 414101088, 414232672, 414635520, 415036456, 417785440, 418969696, 428928736, 429575368, 429964928, 430364896, 430766792, 431154376, 434697856, 446752896, 447400616, 447524040, 447918792, 448058536, 448722560, 449244896, 450024136, 450425056, 451208392, 452655816, 464578144, 467066880, 468382760, 518053888, 520027648, 679510016, 679929440, 680174120, 680313928, 680836136, 681113696, 682141696, 682544736, 683862568, 684247040, 685168128, 685569064, 687799808, 697755776, 698002632, 698141352, 699071656, 700366976, 700897504, 701299400, 715827880, 715967688, 717285504, 717933224, 718591144, 719255168, 721222824, 733790760, 734321224, 734984288, 751234784, 751619272, 752014024, 752414944, 753198280, 754645704, 769056768, 770372648, 786884192, 788068448, 1019396648, 1019797504, 1020722688, 1022028328, 1037627104, 1055451264, 1753393832, 1753778304, 1754197728, 1754699392, 1754976968, 1756161224, 1757331072, 1760094336, 1772019712, 1773988392, 1789847136, 1791549440, 1793780264, 1807673472, 1809379040, 1861152480]
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Finding the next row would require looping through the  (slightly more than a billion) 6-ary royal Boolean functions.
| triangle of king indices
|
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These are the index numbers of the kings in the respective sequence of nobles.
It seems, that each row is a subset of the next.
0
1
2
3
4
|
[0]
[0]
[0]
[0, 2]
[0, 2, 6, 8, 14, 22, 26, 42, 44, 104, 110]
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| row 5 of length 272: 0, 2, 6 ... 27582, 27608, 28398
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[0, 2, 6, 8, 10, 14, 22, 24, 26, 40, 42, 44, 46, 62, 104, 110, 126, 128, 134, 138, 152, 158, 168, 174, 254, 278, 280, 282, 286, 296, 298, 302, 316, 362, 382, 386, 392, 406, 410, 426, 552, 554, 556, 558, 572, 576, 578, 584, 590, 596, 598, 602, 604, 606, 618, 620, 636, 638, 642, 644, 648, 654, 662, 666, 668, 682, 684, 704, 714, 724, 734, 764, 830, 856, 862, 872, 878, 892, 896, 902, 906, 916, 920, 926, 936, 956, 964, 974, 1634, 1640, 1646, 1654, 1656, 1658, 1664, 1670, 1674, 1682, 1688, 1694, 1698, 1704, 1710, 1712, 1718, 1724, 1766, 1784, 1912, 1918, 1922, 1928, 1934, 1936, 1946, 1952, 1958, 1964, 1970, 2024, 2178, 2184, 2190, 2192, 2198, 2202, 2208, 2214, 2220, 2226, 2232, 2238, 2280, 2294, 2450, 2462, 2466, 2472, 2478, 2492, 2534, 2722, 2724, 2734, 2736, 2746, 2748, 2760, 2774, 2780, 2794, 2804, 3006, 3032, 3044, 3822, 3824, 5736, 5738, 5758, 5762, 5768, 5774, 5782, 5786, 5804, 5822, 5864, 6016, 6022, 6026, 6046, 6076, 6272, 6278, 6282, 6290, 6296, 6302, 6306, 6312, 6318, 6320, 6326, 6332, 6374, 6392, 6544, 6554, 6560, 6566, 6572, 6578, 6632, 6816, 6826, 6828, 6834, 6836, 6846, 6854, 6866, 6872, 6884, 6906, 7088, 7126, 7146, 7904, 7934, 10368, 10374, 10378, 10380, 10388, 10392, 10408, 10414, 10434, 10440, 10454, 10460, 10494, 10646, 10650, 10652, 10666, 10686, 10694, 10700, 10922, 10924, 10944, 10954, 10964, 10974, 11004, 11196, 11204, 11214, 11462, 11468, 11474, 11480, 11492, 11514, 11734, 11754, 12006, 12024, 15554, 15560, 15574, 15594, 15832, 16104, 26754, 26760, 26766, 26774, 26778, 26796, 26814, 26856, 27038, 27068, 27310, 27336, 27370, 27582, 27608, 28398]
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