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URL: https://oeis.org/A301976

⇱ A301976 - OEIS

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A301976
Number of no-leaf subgraphs of the 3 X n grid.
5
1, 5, 43, 463, 5193, 58653, 663203, 7500343, 84825873, 959351093, 10849935003, 122709094303, 1387798370393, 15695530423373, 177511143297043, 2007591024144903, 22705175829637153, 256787863292718693, 2904183928335418123, 32845338488555237743
OFFSET
1,2
COMMENTS
Also, the number of ways to lay unit-length matchsticks on a 3 X n grid of points in such a way that no end is "orphaned".
Conjecture: a(n) mod 10 = 3 for n > 2.
LINKS
FORMULA
Conjectures from Colin Barker, Mar 30 2018: (Start)
G.f.: x*(1 + x)*(1 - 8*x - 3*x^2) / (1 - 12*x + 6*x^2 + 20*x^3 + 5*x^4).
a(n) = 12*a(n-1) - 6*a(n-2) - 20*a(n-3) - 5*a(n-4) for n>4.
(End)
EXAMPLE
Three of the a(4) = 463 subgraphs of the 3 X 4 grid with no leaf vertices are
+---+ +---+ + + +---+ + + +---+
| | | | | | | |
+---+---+ +, + +---+---+, and +---+ +---+.
| | | | | | |
+---+---+---+ + +---+ + +---+ + +
CROSSREFS
A093129 is analogous for 2 X (n+1) grids.
Sequence in context: A239265 A369023 A274666 * A083070 A191802 A092471
KEYWORD
nonn
AUTHOR
Peter Kagey, Mar 29 2018
STATUS
approved