cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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).

Original entry on oeis.org

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

Views

Author

Pontus von Brömssen and Peter Kagey, May 28 2025

Keywords

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

Crossrefs

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

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).

Original entry on oeis.org

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

Views

Author

Pontus von Brömssen and Peter Kagey, May 28 2025

Keywords

Comments

Two faces are connected if they share an edge.
Equivalently, T(n,k) is the number of connected induced k-vertex subgraphs of the 1-skeleton of the dual of the n-th Johnson solid, up to symmetries of that dual.

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

Crossrefs

Cf. A242731 (row lengths), A384376, A384378, A384381 (row sums).

A384379 Number of connected subsets of edges (or edge-induced subgraphs, or polysticks) of the n-th Johnson solid, up to symmetries of that solid.

Original entry on oeis.org

44, 111, 3402, 56848, 1000431
Offset: 1

Views

Author

Pontus von Brömssen and Peter Kagey, May 28 2025

Keywords

Comments

The empty set is not included in the counts.

Links

Crossrefs

Row sums of A384378.
Cf. A343210, A384377, A384381.
Showing 1-3 of 3 results.

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