A298198 - OEIS

%I #17 Feb 16 2025 08:33:53

%S 4,40,320,2368,16832,116608,793088,5318656,35271680,231786496,

%T 1511653376,9795518464,63126683648,404881506304,2586017398784,

%U 16456474427392,104381066510336,660139718213632,4163958223142912,26202468819927040,164527129801785344

%N Number of Eulerian cycles in the graph Cartesian product of C_n and a double edge.

%C When n = 2 the graph is the Cartesian product of two double edges.

%C a(n) is divisible by 2^(n + 1).

%H Andrew Howroyd, <a href="/A298198/b298198.txt">Table of n, a(n) for n = 1..500</a>

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14, -60, 72).

%F a(n) = 14*a(n-1) - 60*a(n-2) + 72*a(n-3) for n > 3.

%F G.f.: 4*x*(1 - 4*x)/((1 - 2*x)*(1 - 6*x)^2).

%o (PARI) Vec(4*(1 - 4*x)/((1 - 2*x)*(1 - 6*x)^2) + O(x^30))

%Y Row 2 of A298117.

%K nonn,changed

%O 1,1

%A _Andrew Howroyd_, Jan 14 2018