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

1,2

Comments

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

Links

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

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)

Example

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

Crossrefs

Cf. A020876, A301976.

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

Sequence in context: A148099 A007579 A239078 * A007123 A220871 A007578

Adjacent sequences: A303927 A303928 A303929 * A303931 A303932 A303933

Keyword

nonn

Author

Peter Kagey, May 02 2018

Status

approved