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A303930 Number of no-leaf subgraphs of the 2 X n grid up to horizontal and vertical reflection. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 16 19:49 EST 2019. Contains 319206 sequences. (Running on oeis4.)