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Number of closed walks of length 2n on the Heawood graph from a given node.
1

%I #14 Sep 08 2022 08:45:19

%S 1,3,15,111,951,8463,75975,683391,6149751,55346223,498112935,

%T 4483010271,40347080151,363123696783,3268113221895,29413018898751,

%U 264717169892151,2382454528636143,21442090756938855

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

%H G. C. Greubel, <a href="/A109498/b109498.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Heawood_graph">Heawood graph</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-18).

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

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

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

%t 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 *)

%o (PARI) x='x+O('x^30); Vec((1 - 8*x)/((9*x - 1)*(2*x - 1))) \\ _G. C. Greubel_, Dec 30 2017

%o (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

%K nonn,easy

%O 0,2

%A _Mitch Harris_, Jun 30 2005