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%I #20 Feb 07 2023 12:43:28
%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.: (1/20)*(-4 + 5/(1-t) + 1/(1-3*t) + 4/(1+2*t) - 6/(1-5*t^2)).
%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/((1-x)*(1+2*x)*(1-3*x)*(1-5*x^2)). - _Colin Barker_, Dec 21 2014
%F E.g.f.: (1/20)*(4*exp(-2*x) + 5*exp(x) + exp(3*x) - 6*cosh(sqrt(5)*x) - 4). - _G. C. Greubel_, Feb 07 2023
%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
%o (Magma) [Round((5 +3^n +4*(-2)^n -3*(1+(-1)^n)*5^(n/2))/20): n in [0..30]]; // _G. C. Greubel_, Feb 07 2023
%o (SageMath)
%o def A054883(n): return (5 +3^n +4*(-2)^n -3*(1+(-1)^n)*5^(n/2))/20 -int(n==0)/5
%o [A054883(n) for n in range(41)] # _G. C. Greubel_, Feb 07 2023
%Y Cf. A054881, A054882, A054884, A054885.
%K nonn,easy
%O 0,6
%A Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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