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%I
%S 0,14,32,150,492,1894,6724,24854,89972,329238,1197972,4372054,
%T 15930580,58096214,211770452,772129110,2814859092,10262536534,
%U 37414140244,136403674454,497291840852,1813006427478,6609762501972,24097566365014
%N 7 X 7 matrix Matrov of seven vertex Fano Plane: Characteristic polynomial : 12 + 10 x - 24 x^2 - 21 x^3 + 12 x^4 + 12 x^5 - x^7.
%C Limited here to seven connecting lines in the bonding graph.
%D (*http://mathworld.wolfram.com/FanoPlane.html*)
%F M = {{0, 1, 0, 0, 0, 1, 1}, {1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 0, 1}, {0, 0, 1, 0, 1, 0, 1}, {0, 0, 0, 1, 0, 1, 1}, {1, 0, 0, 0, 1, 0, 1}, {1, 1, 1, 1, 1, 1, 0}} v[1] = {0, 1, 1, 2, 3, 5, 8} v[n_] := v[n] = M.v[n - 1] a(n) =v[n][[1]].
%F Empirical G.f.: 2*x*(7+16*x-2*x^2-14*x^3)/((1-x)*(1+x)*(1+2*x)*(1-2*x-6*x^2)). [Colin Barker, Mar 26 2012]
%t M = {{0, 1, 0, 0, 0, 1, 1}, {1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 0, 1}, {0, 0, 1, 0, 1, 0, 1}, {0, 0, 0, 1, 0, 1, 1}, {1, 0, 0, 0, 1, 0, 1}, {1, 1, 1, 1, 1, 1, 0}} v[1] = {0, 1, 1, 2, 3, 5, 8} v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}]
%Y Cf. A111384.
%K nonn
%O 0,2
%A _Roger L. Bagula_, Aug 12 2006
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