A307871 - OEIS

%I #9 Feb 16 2025 08:33:55

%S 0,6,1365,210541386790

%N Number of (undirected) paths in the n-odd graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphPath.html">Graph Path</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OddGraph.html">Odd Graph</a>

%e O_1 is K_1 which has no edges, so a(1) = 0.

%e O_2 is K_3 which has 3 undirected paths of length one and 3 of length two, so a(2) = 6.

%e 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.

%K nonn,more

%O 1,2

%A _Eric W. Weisstein_, May 02 2019