O_1 is K_1 which has no edges, so a(1) = 0.
O_2 is K_3 which has 3 undirected paths of length one and 3 of length two, so a(2) = 6.
O_3 is the Petersen graph with path polynomial P(x) = 15*x + 30*x^2 + 60*x^3 + 120*x^4 + 180*x^5 + 240*x^6 + 300*x^7 + 300*x^8 + 120*x^9, so a(3) = P(1) = 1365.
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