%I #5 Mar 30 2012 17:25:28
%S 1,3,5,15,37,111,317,951,2821,8463,25325,75975,227797,683391,2049917,
%T 6149751,18448741,55346223
%N Sequence generated by incidence matrix of the Fano plane, PG(2,2).
%C a(n)/a(n-1) tends to 3, an eigenvalue of the matrix.
%D Mathworld (Projective plane).
%F Let X = the 7x7 incidence matrix of the Fano plane PG(2,2): [1,1,1,0,0,0,0; 1,0,0,1,1,0,0; 1,0,0,0,0,1,1; 0,1,0,1,0,1,0; 0,1,0,0,1,0,1; 0,0,1,1,0,0,1; 0,0,1,0,1,1,0]. a(n) = the upper left term in X^n.
%F Empirical a(n)=3*a(n-1)+2*a(n-2)-6*a(n-3). G.f.: x*(1-6*x^2)/(1-3*x-2*x^2+6*x^3). [Colin Barker, Jan 26 2012]
%e a(5) = 37, the upper left term of X^5.
%K nonn
%O 1,2
%A _Gary W. Adamson_, Feb 28 2008