A303930 Number of no-leaf subgraphs of the 2 X n grid up to horizontal and vertical reflection.

1, 2, 4, 10, 26, 76, 232, 750, 2493, 8514, 29524, 103708, 367225, 1308542, 4682276, 16807286, 60462082, 217855460, 785863048, 2837177434, 10249053629, 37039804078, 133902392980, 484178868612, 1751030978481, 6333341963706, 22909148647012, 82872738727330

Offset: 1

Author

Peter Kagey, May 02 2018

Keywords

• nonn

Comments

The limit lim_{n -> infinity} A020876(n - 1)/a(n) = 4.

Examples

			For n = 4 the a(4) = 10 subgraphs of the 2 X 4 grid are:
+   +   +   +  +---+   +   +  +   +---+   +
               |   |              |   |
+   +   +   +, +---+   +   +, +   +---+   +,
+---+   +---+  +---+---+   +  +---+---+---+
|   |   |   |  |       |      |       |   |
+---+   +---+, +---+---+   +, +---+---+---+,
+---+---+---+  +---+---+---+  +---+---+---+
|           |  |   |   |   |  |   |   |   |
+---+---+---+, +---+---+---+, +---+   +---+, and
+---+---+   +
|   |   |
+---+---+   +.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A020876, A301976.

A093129 is analogous for 2 X (n+1) grids where reflections are considered distinct.

Formula

Conjectures from Colin Barker, May 03 2018: (Start)

G.f.: x*(1 - 6*x + 4*x^2 + 30*x^3 - 45*x^4 - 22*x^5 + 60*x^6 - 20*x^7) / ((1 - 3*x + x^2)*(1 - 5*x + 5*x^2)*(1 - 5*x^2 + 5*x^4)).

a(n) = 8*a(n-1) - 16*a(n-2) - 20*a(n-3) + 95*a(n-4) - 60*a(n-5) - 80*a(n-6) + 100*a(n-7) - 25*a(n-8) for n>8.

(End)