A368190 - OEIS

%I #18 Dec 30 2023 16:18:07

%S 0,1,11,249,74835,5890739121,34755832523270764251,

%T 1207969003612007237832573159205646499369,

%U 1459189113687796591938380205390010178829792070192521048490799792728844237848995

%N Number of (undirected) cycles in the n-Dorogovtsev-Goltsev-Mendes graph.

%C Using the indexing convention that DGM(0) = P_2.

%C For n > 0, DGM(n) contains a unique longest cycle of length 3*2^(n-1).

%H Andrew Howroyd, <a href="/A368190/b368190.txt">Table of n, a(n) for n = 0..11</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Dorogovtsev-Goltsev-MendesGraph.html">Dorogovtsev-Goltsev-Mendes Graph</a>.

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

%F a(n) = 3*a(n-1) + A007018(n-1)^3 for n > 0. - _Andrew Howroyd_, Dec 30 2023

%o (PARI) a(n) = {my(t=0,b=1); for(k=1, n, t = 3*t + b^3; b += b^2); t} \\ _Andrew Howroyd_, Dec 30 2023

%Y Cf. A007018, A368456, A367967 (5-cycles), A367968 (6-cycles).

%K nonn

%O 0,3

%A _Eric W. Weisstein_, Dec 16 2023

%E Offset corrected and a(5) from _Eric W. Weisstein_, Dec 29 2023

%E Terms a(6) and beyond from _Andrew Howroyd_, Dec 30 2023