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A320099
Number of no-leaf subgraphs of the 5 X n grid.
2
1, 50, 5193, 583199, 65485654, 7354266811, 825905301851, 92751581627976, 10416273692997679, 1169777980482365913, 131369486228240893660, 14753177269494392259423, 1656824927874469183283433, 186066281959642930757881316, 20895787297635543757965741097
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
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
A093129 is analogous for 2 X (n+1) grids.
A301976 is analogous for 3 X n grids.
A320097 is analogous for 4 X n grids.
Sequence in context: A174756 A231937 A230477 * A115436 A184555 A301992
KEYWORD
nonn
AUTHOR
Peter Kagey, Oct 05 2018
STATUS
approved