A384380 Irregular triangle read by rows: T(n,k) is the number of connected subsets of k faces (or polyforms) of the n-th Johnson solid, up to symmetries of that solid; 1 <= n <= 92, 1 <= k <= A242731(n).
2, 2, 3, 2, 1, 2, 2, 3, 3, 2, 1, 4, 4, 9, 14, 14, 9, 4, 1, 4, 4, 12, 20, 32, 30, 23, 11, 4, 1, 4, 4, 13, 29, 54, 75, 75, 55, 31, 12, 4, 1, 5, 5, 17, 43, 118, 285, 595, 992, 1320, 1348, 1045, 603, 262, 86, 22, 5, 1, 3, 4, 6, 7, 6, 3, 1, 3, 4, 7, 12, 17, 16, 9, 3, 1
Offset: 1
Examples
Triangle begins: n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ---+---------------------------------------------------------------------- 1 | 2 2 3 2 1 2 | 2 2 3 3 2 1 3 | 4 4 9 14 14 9 4 1 4 | 4 4 12 20 32 30 23 11 4 1 5 | 4 4 13 29 54 75 75 55 31 12 4 1 6 | 5 5 17 43 118 285 595 992 1320 1348 1045 603 262 86 22 5 1 7 | 3 4 6 7 6 3 1 8 | 3 4 7 12 17 16 9 3 1 9 | 3 4 7 13 24 35 36 22 9 3 1 10 | 4 4 8 15 28 47 81 102 87 45 16 4 1 11 | 4 4 8 17 35 71 139 252 378 429 340 183 67 18 4 1 12 | 1 2 2 3 1 1 13 | 1 2 2 5 6 10 7 5 1 1 14 | 2 3 5 7 10 9 6 2 1 15 | 2 3 5 11 19 31 38 38 20 10 2 1 16 | 2 3 5 11 23 45 82 126 154 130 77 30 10 2 1 17 | 2 3 4 10 16 35 61 120 180 237 194 117 40 13 2 1 18 | 6 7 17 36 81 165 300 386 337 197 82 25 6 1 19 | 6 7 20 44 121 290 701 1403 2359 3047 2975 2110 1106 435 131 31 6 1
Links
- Pontus von Brömssen, Table of n, a(n) for n = 1..341 (first 24 rows)
- Eric Weisstein's World of Mathematics, Johnson Solid.
- Wikipedia, List of Johnson solids.
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