A384380 -id:A384380 - cp's OEIS frontend

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

Pontus von Brömssen and Peter Kagey, May 28 2025

			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

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.

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

A384378 Irregular triangle read by rows: T(n,k) is the number of connected subsets of k edges (or polysticks) of the n-th Johnson solid, up to symmetries of that solid; 1 <= n <= 92, 1 <= k <= A242732(n).

Original entry on oeis.org

2, 4, 7, 12, 10, 6, 2, 1, 2, 4, 9, 17, 28, 25, 16, 7, 2, 1, 4, 7, 20, 47, 123, 274, 531, 779, 758, 504, 241, 87, 22, 4, 1, 4, 7, 20, 51, 144, 382, 990, 2332, 4873, 8546, 11776, 11733, 8529, 4673, 1957, 639, 156, 31, 4, 1

Offset: 1

Pontus von Brömssen and Peter Kagey, May 28 2025

			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  4  7 12  10   6   2    1
  2  | 2  4  9 17  28  25  16    7    2    1
  3  | 4  7 20 47 123 274 531  779  758  504   241    87   22    4    1
  4  | 4  7 20 51 144 382 990 2332 4873 8546 11776 11733 8529 4673 1957 639 156 31  4  1

Pontus von Brömssen, Table of n, a(n) for n = 1..78 (first 5 rows)
Eric Weisstein's World of Mathematics, Johnson Solid.
Wikipedia, List of Johnson solids.

Cf. A242732 (row lengths), A384376, A384379 (row sums), A384380.

A384381 Number of connected subsets of faces (or polyforms) of the n-th Johnson solid, up to symmetries of that solid.

Original entry on oeis.org

10, 13, 59, 141, 357, 6752, 30, 72, 157, 442, 1950, 10, 40, 45, 180, 701, 1035, 1646, 14793, 153721, 3920545, 42372, 1495651, 59265752

Offset: 1

Pontus von Brömssen and Peter Kagey, May 28 2025

Two faces are connected if they share an edge.

The empty set is not included in the counts.

Eric Weisstein's World of Mathematics, Johnson Solid.
Wikipedia, List of Johnson solids.

Row sums of A384380.

Cf. A384377, A384379.

cp's OEIS Frontend

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).

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A384378 Irregular triangle read by rows: T(n,k) is the number of connected subsets of k edges (or polysticks) of the n-th Johnson solid, up to symmetries of that solid; 1 <= n <= 92, 1 <= k <= A242732(n).

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A384381 Number of connected subsets of faces (or polyforms) of the n-th Johnson solid, up to symmetries of that solid.

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