

A301976


Number of noleaf 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
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OFFSET

1,2


COMMENTS

Also, the number of ways to lay unitlength 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

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(n1)  6*a(n2)  20*a(n3)  5*a(n4) 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.


KEYWORD

nonn


AUTHOR



STATUS

approved



