OFFSET
1,2
COMMENTS
Also, the number of ways to lay unit-length matchsticks on a 5 X n grid of points in such a way that no end is "orphaned".
LINKS
Peter Kagey, Table of n, a(n) for n = 1..488
FORMULA
Conjecture: a(n) = 103*a(n-1) + 1063*a(n-2) - 1873*a(n-3) - 20274*a(n-4) + 44071*a(n-5) - 10365*a(n-6) - 20208*a(n-7) + 5959*a(n-8) + 2300*a(n-9) - 500*a(n-10) for n > 10.
EXAMPLE
Three of the a(3) = 5193 subgraphs of the 5 X 3 grid with no leaf vertices are:
+---+---+ + + + + +---+
| | | | |
+---+---+ +---+---+ + +---+
| | |, | | |, and .
+---+---+ + +---+ +---+ +
| | | | | | |
+---+---+ +---+ + +---+---+
| | | | |
+---+---+ + + + + +---+
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Kagey, Oct 05 2018
STATUS
approved