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URL: https://oeis.org/A303930

⇱ A303930 - OEIS

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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
OFFSET
1,2
COMMENTS
The limit lim_{n -> infinity} A020876(n - 1)/a(n) = 4.
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
A093129 is analogous for 2 X (n+1) grids where reflections are considered distinct.
Sequence in context: A148099 A007579 A239078 * A007123 A220871 A007578
KEYWORD
nonn
AUTHOR
Peter Kagey, May 02 2018
STATUS
approved