cp's OEIS Frontend

A054884 Number of closed walks of length n along the edges of an icosahedron based at a vertex.

%I A054884 #36 Feb 08 2023 07:43:01
%S A054884 1,0,5,10,65,260,1365,6510,32865,162760,815365,4069010,20352865,
%T A054884 101725260,508665365,2543131510,12715852865,63578287760,317892415365,
%U A054884 1589457194010,7947290852865,39736429850260
%N A054884 Number of closed walks of length n along the edges of an icosahedron based at a vertex.
%H A054884 Vincenzo Librandi, <a href="/A054884/b054884.txt">Table of n, a(n) for n = 0..1000</a>
%H A054884 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,10,-20,-25).
%F A054884 G.f.: (1/12)*(1/(1-5*t) + 5/(1+t) + 6/(1-5*t^2)).
%F A054884 a(n) = (5^n + (-1)^n*5 + 3*(1 + (-1)^n)*sqrt(5)^n)/12.
%F A054884 a(n+1) = 5 * A030517(n) for n > 0.
%F A054884 a(n) = 4*a(n-1) + 10*a(n-2) - 20*a(n-3) - 25*a(n-4). - _François Marques_, Jul 10 2021
%F A054884 E.g.f.: (1/12)*(5*exp(-x) + exp(5*x) + 6*cosh(sqrt(5)*x)). - _G. C. Greubel_, Feb 07 2023
%t A054884 LinearRecurrence[{4,10,-20,-25},{1,0,5,10},30] (* _Harvey P. Dale_, May 02 2022 *)
%o A054884 (Magma) [Floor((5^n+(-1)^n*5+3*(1+(-1)^n)*Sqrt(5)^n)/12): n in [0..30]]; // _Vincenzo Librandi_, Aug 24 2011
%o A054884 (PARI) a(n) = if(n%2, 5^n-5, 5^n+5+6*5^(n/2))/12; \\ _François Marques_, Jul 11 2021
%o A054884 (SageMath)
%o A054884 def A054884(n): return (5^n + 5*(-1)^n + 3*(1 + (-1)^n)*5^(n/2))/12
%o A054884 [A054884(n) for n in range(41)] # _G. C. Greubel_, Feb 07 2023
%Y A054884 Cf. A030517, A030518, A054881, A054882, A054883, A054885.
%K A054884 nonn,walk,easy
%O A054884 0,3
%A A054884 Paolo Dominici (pl.dm(AT)libero.it), May 23 2000