A320099 Number of no-leaf subgraphs of the 5 X n grid.

1, 50, 5193, 583199, 65485654, 7354266811, 825905301851, 92751581627976, 10416273692997679, 1169777980482365913, 131369486228240893660, 14753177269494392259423, 1656824927874469183283433, 186066281959642930757881316, 20895787297635543757965741097

Offset: 1

Author

Peter Kagey, Oct 05 2018

Keywords

• nonn

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".

Examples

			Three of the a(3) = 5193 subgraphs of the 5 X 3 grid with no leaf vertices are:
+---+---+      +   +   +      +   +---+
|   |   |                         |   |
+---+---+      +---+---+      +   +---+
|   |   |,     |   |   |, and          .
+---+---+      +   +---+      +---+   +
|   |   |      |   |          |   |
+---+---+      +---+   +      +---+---+
|   |   |                         |   |
+---+---+      +   +   +      +   +---+
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..488

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.

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.