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

1,1

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).

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)).

Mathematica

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

Prog

(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))

Crossrefs

Row 4 of A298119.

Cf. A006240, A298197.

Sequence in context: A221685 A203721 A231527 * A234443 A234436 A297461

Adjacent sequences: A298198 A298199 A298200 * A298202 A298203 A298204

Keyword

nonn

Author

Andrew Howroyd, Jan 14 2018

Status

approved