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%I
%S 0,0,0,0,0,6,12,84,192,882,2220,8448,22704,78078,218988,710892,
%T 2048256,6430794,18837516,58008216,171619248,522598230,1555243404,
%U 4705481220,14051590080,42357719586,126740502252,381253030704,1142062255152,3431411494062
%N Number of walks of length n along the edges of a dodecahedron between two opposite vertices.
%H Colin Barker, <a href="/A054883/b054883.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,10,-16,-25,30).
%F G.f.: -1/5-1/4/(t-1)-1/20/(3*t-1)+1/5/(2*t+1)+3/10/(5*t^2-1).
%F a(n) = (5+3^n+(-1)^n*2^(n+2)-3*(1+(-1)^n)*sqrt(5)^n)/20 for n>0.
%F G.f.: -6*x^5 / ((x-1)*(2*x+1)*(3*x-1)*(5*x^2-1)). - _Colin Barker_, Dec 21 2014
%t LinearRecurrence[{2,10,-16,-25,30},{0,0,0,0,0,6},30] (* _Harvey P. Dale_, Nov 13 2021 *)
%o (PARI) concat([0,0,0,0,0], Vec(-6*x^5/((x-1)*(2*x+1)*(3*x-1)*(5*x^2-1)) + O(x^100))) \\ _Colin Barker_, Dec 21 2014
%K nonn,easy
%O 0,6
%A Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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