A298201 Number of Eulerian orientations of the torus grid graph C_4 X C_n.

32, 114, 548, 2970, 16892, 98466, 583412, 3500970, 21232556, 129930354, 801132452, 4970993658, 31006439132, 194231313474, 1220944803668, 7696445791050, 48625129598732, 307759067766546, 1950657679387652, 12377791111168410, 78613025212107836, 499635602835227874

Offset: 1

Author

Andrew Howroyd, Jan 14 2018

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Torus Grid Graph
• Index entries for linear recurrences with constant coefficients, signature (15,-77,161,-138,40).

Crossrefs

Row 4 of A298119.

Cf. A006240, A298197.

Programs

Mathematica

LinearRecurrence[{15, -77, 161, -138, 40}, {32, 114, 548, 2970, 16892}, 22] (* Jean-François Alcover, Sep 21 2019 *)

PARI

Vec(2*(16 - 183*x + 651*x^2 - 812*x^3 + 300*x^4)/((1 - x)*(1 - 2*x)*(1 - 5*x)*(1 - 7*x + 4*x^2)) + O(x^25))

Formula

a(n) = 15*a(n-1) - 77*a(n-2) + 161*a(n-3) - 138*a(n-4) + 40*a(n-5).

G.f.: 2*x*(16 - 183*x + 651*x^2 - 812*x^3 + 300*x^4)/((1 - x)*(1 - 2*x)*(1 - 5*x)*(1 - 7*x + 4*x^2)).