|
%I #21 Feb 19 2015 14:26:57
%S 1,2,14,322,23858,5735478,4468252414,11282914491066,92343922085798834,
%T 2449629600675855540670,210618917058297166847778158,
%U 58694743562963266347581955456602,53015873227026172656988353687982082782,155209215810704933798454506348361943868443334
%N Number of 0/1 colorings of an n X n square for which no 2 by 2 subsquare is monochromatic.
%C 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.
%H Alois P. Heinz, <a href="/A133130/b133130.txt">Table of n, a(n) for n = 0..15</a>
%e a(2) = 14 because 2 of the 16 unrestricted colorings are monochromatic.
%Y Cf. A055099.
%Y Main diagonal of A181245.
%K nonn
%O 0,2
%A _Victor S. Miller_, Sep 19 2007
%E a(0)-a(1), a(11)-a(13) from _Alois P. Heinz_, Feb 18 2015
| 