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%I #22 Feb 02 2022 03:58:58
%S 1,3,15,65,325,1575,7875,39125,195625,976875,4884375,24415625,
%T 122078125,610359375,3051796875,15258828125,76294140625,381469921875,
%U 1907349609375,9536744140625,47683720703125
%N a(n) = (5^n + 5^floor(n/2))/2.
%H Vincenzo Librandi, <a href="/A001447/b001447.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,5,-25).
%F a(n) = 5*a(n-1) + 5*a(n-2) - 25*a(n-3); a(0)=1, a(1)=3, a(2)=15. - _Harvey P. Dale_, May 05 2011
%F G.f.: (1 - 2x - 5x^2)/(1 - 5x - 5x^2 + 25x^3). - _Harvey P. Dale_, May 05 2011
%t Table[(5^n+5^Floor[n/2])/2,{n,0,20}] (* or *) LinearRecurrence[ {5,5,-25}, {1,3,15}, 50](* _Harvey P. Dale_, May 05 2011 *)
%o (PARI) a(n)=(5^n+5^(n\2))/2 \\ _Charles R Greathouse IV_, Apr 17 2012
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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