cp's OEIS Frontend

A054882 Closed walks of length n along the edges of a dodecahedron based at a vertex.

%I A054882 #20 Feb 07 2023 12:43:32
%S A054882 1,0,3,0,15,6,87,84,567,882,4095,8448,32079,78078,265863,710892,
%T A054882 2282631,6430794,20009391,58008216,177478623,522598230,1584540279,
%U A054882 4705481220,14198074455,42357719586,127472924127,381253030704
%N A054882 Closed walks of length n along the edges of a dodecahedron based at a vertex.
%H A054882 Vincenzo Librandi, <a href="/A054882/b054882.txt">Table of n, a(n) for n = 0..1000</a>
%H A054882 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,10,-16,-25,30).
%F A054882 G.f.: (1/20)*(4 + 5/(1-x) + 1/(1-3*x) + 4/(1+2*x) + 6/(1-5*x^2)).
%F A054882 G.f.: (1 - 2*x - 7*x^2 + 10*x^3 + 10*x^4 - 6*x^5)/((1-x)*(1+2*x)*(1-3*x)*(1-5*x^2)).
%F A054882 a(n) = (5 + 3^n + (-1)^n*2^(n+2) + 3*(1+(-1)^n)*sqrt(5)^n + 4*0^n)/20.
%F A054882 E.g.f.: (1/20)*(4 + 4*exp(-2*x) + 5*exp(x) + exp(3*x) + 6*cosh(sqrt(5)*x)). - _G. C. Greubel_, Feb 07 2023
%t A054882 LinearRecurrence[{2,10,-16,-25,30}, {1,0,3,0,15,6}, 41] (* _G. C. Greubel_, Feb 07 2023 *)
%o A054882 (Magma) [Ceiling((5+3^n+(-1)^n*2^(n+2)+3*(1+(-1)^n)*Sqrt(5)^n)/20): n in [0..30]]; // _Vincenzo Librandi_, Aug 24 2011
%o A054882 (SageMath)
%o A054882 def A054882(n): return (5+3^n+4*(-2)^n+3*(1+(-1)^n)*5^(n/2)+4*0^n)/20
%o A054882 [A054882(n) for n in range(41)] # _G. C. Greubel_, Feb 07 2023
%Y A054882 Cf. A054881, A054883, A054884, A054885.
%K A054882 nonn,easy,walk
%O A054882 0,3
%A A054882 Paolo Dominici (pl.dm(AT)libero.it), May 23 2000