A384376 Irregular triangle read by rows: T(n,k) is the number of connected induced k-vertex subgraphs of the 1-skeleton of the n-th Johnson solid, up to symmetries of that solid; 1 <= n <= 92, 1 <= k <= A242733(n).

2, 2, 3, 2, 1, 2, 2, 3, 3, 2, 1, 2, 4, 6, 10, 14, 15, 8, 2, 1, 2, 4, 6, 13, 21, 37, 47, 51, 28, 12, 2, 1, 2, 4, 6, 13, 25, 49, 86, 136, 177, 174, 118, 47, 14, 2, 1, 3, 5, 9, 18, 39, 79, 168, 335, 646, 1147, 1843, 2548, 2908, 2420, 1300, 473, 121, 24, 3, 1, 3, 4, 6, 7, 6, 3, 1

Offset: 1

Author

Pontus von Brömssen and Peter Kagey, May 28 2025

Keywords

• nonn
• tabf
• fini

Examples

			Triangle begins:
  n\k| 1  2  3  4  5   6   7   8    9   10   11   12   13   14   15  16  17 18 19 20
  ---+------------------------------------------------------------------------------
   1 | 2  2  3  2  1
   2 | 2  2  3  3  2   1
   3 | 2  4  6 10 14  15   8   2    1
   4 | 2  4  6 13 21  37  47  51   28   12    2    1
   5 | 2  4  6 13 25  49  86 136  177  174  118   47   14    2    1
   6 | 3  5  9 18 39  79 168 335  646 1147 1843 2548 2908 2420 1300 473 121 24  3  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 | 3  4  9 16 21  16   8   3    1
  11 | 3  4  9 18 36  49  41  23    9    3    1
  12 | 2  2  3  2  1
  13 | 2  2  4  5  4   2   1
  14 | 2  3  4  7  6   6   2   1
  15 | 2  3  5 10 15  20  13   8    2    1
  16 | 2  3  5 11 20  38  41  36   16    8    2    1
  17 | 2  3  6 13 19  21  12   7    2    1
  18 | 3  7 12 29 60 134 255 425  523  420  223   80   21    3    1
  19 | 3  7 12 32 69 174 393 899 1856 3512 5517 6874 6173 3964 1789 615 146 30  3  1
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..638 (first 39 rows)
• Eric Weisstein's World of Mathematics, Johnson Solid.
• Wikipedia, List of Johnson solids.

Crossrefs

Cf. A242733 (row lengths), A384377 (row sums), A384378, A384380.