A298198 Number of Eulerian cycles in the graph Cartesian product of C_n and a double edge.

4, 40, 320, 2368, 16832, 116608, 793088, 5318656, 35271680, 231786496, 1511653376, 9795518464, 63126683648, 404881506304, 2586017398784, 16456474427392, 104381066510336, 660139718213632, 4163958223142912, 26202468819927040, 164527129801785344

Offset: 1

Author

Andrew Howroyd, Jan 14 2018

Keywords

• nonn

Comments

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

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• Eric Weisstein's World of Mathematics, Eulerian Cycle
• Index entries for linear recurrences with constant coefficients, signature (14, -60, 72).

Crossrefs

Row 2 of A298117.

Programs

PARI

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

Formula

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

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