A133130 Number of 0/1 colorings of an n X n square for which no 2 by 2 subsquare is monochromatic.

1, 2, 14, 322, 23858, 5735478, 4468252414, 11282914491066, 92343922085798834, 2449629600675855540670, 210618917058297166847778158, 58694743562963266347581955456602, 53015873227026172656988353687982082782, 155209215810704933798454506348361943868443334

Offset: 0

Author

Victor S. Miller, Sep 19 2007

Keywords

• nonn

Comments

For each n we define an undirected labeled graph (with self loops), where the vertices are labeled with strings from {0,1}^n and there is an edge between two vertices exactly when we can form a 2 X n rectangle whose rows are the two labels and the 2 X n rectangle has no monochromatic 2 X 2 subsquares. a(n) is the number of walks of length n in this graph. Thus it is the sum of all of the entries of A^n, where A is the adjacency matrix of the graph.

Examples

			a(2) = 14 because 2 of the 16 unrestricted colorings are monochromatic.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..15

Crossrefs

Cf. A055099.

Main diagonal of A181245.

Extensions

a(0)-a(1), a(11)-a(13) from Alois P. Heinz, Feb 18 2015