A109498 Number of closed walks of length 2n on the Heawood graph from a given node.

1, 3, 15, 111, 951, 8463, 75975, 683391, 6149751, 55346223, 498112935, 4483010271, 40347080151, 363123696783, 3268113221895, 29413018898751, 264717169892151, 2382454528636143, 21442090756938855

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Wikipedia, Heawood graph

Index entries for linear recurrences with constant coefficients, signature (11,-18).

Formula

O.g.f.: ( 1-8*x ) / ( (9*x-1)*(2*x-1) ).

a(n) = (9^n + 6*2^n)/7.

a(n) = A106133(n) - 8*A016133(n-1).

Mathematica

CoefficientList[Series[(1 - 8*x)/((9*x - 1)*(2*x - 1)), {x, 0, 50}], x] (* or *) LinearRecurrence[{11, -18}, {1, 3}, 30] (* G. C. Greubel, Dec 30 2017 *)

Prog

(PARI) x='x+O('x^30); Vec((1 - 8*x)/((9*x - 1)*(2*x - 1))) \\ G. C. Greubel, Dec 30 2017
(Magma) I:=[1, 3]; [n le 2 select I[n] else 11*Self(n-1) - 18*Self(n-2): n in [1..30]]; // G. C. Greubel, Dec 30 2017

Crossrefs

Sequence in context: A090355 A083483 A089468 * A142967 A360864 A201339

Adjacent sequences: A109495 A109496 A109497 * A109499 A109500 A109501

Keyword

nonn,easy

Author

Mitch Harris, Jun 30 2005

Status

approved