A320101 Table read by rows: T(n,k) is the number of no-leaf subgraphs of the n X k grid where 1 <= k <= n.

1, 1, 2, 1, 5, 43, 1, 15, 463, 16372, 1, 50, 5193, 583199, 65485654, 1, 175, 58653, 20788249, 7354266811, 2602065897364, 1, 625, 663203, 741026781, 825905301851

Offset

1,3

Links

Table of n, a(n) for n=1..26.

Example

Three of the T(4,3) = 463 subgraphs of the 4 X 3 grid with no leaf vertices are
  +   +---+      +   +   +      +   +---+
      |   |                         |   |
  +---+---+      +---+---+      +   +---+
  |   |    ,     |   |   |, and          .
  +---+   +      +   +---+      +---+   +
  |   |          |   |          |   |
  +---+   +      +---+   +      +---+   +
Table begins:
  n\k|    1    2     3        4          5             6
  ---+---------------------------------------------------
   1 |    1
   2 |    1    2
   3 |    1    5    43
   4 |    1   15   463    16372
   5 |    1   50  5193   583199   65485654
   6 |    1  175 58653 20788249 7354266811 2602065897364

Crossrefs

Cf. A093129, A301976, A320097, A320099.

Sequence in context: A260503 A236436 A187618 * A343018 A323500 A277471

Adjacent sequences: A320098 A320099 A320100 * A320102 A320103 A320104

Keyword

nonn,tabl,more

Author

Peter Kagey, Oct 05 2018

Status

approved