This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A187275 #30 Feb 19 2024 09:57:56
%S A187275 0,5,30,75,300,625,2250,4375,15000,28125,93750,171875,562500,1015625,
%T A187275 3281250,5859375,18750000,33203125,105468750,185546875,585937500,
%U A187275 1025390625,3222656250,5615234375,17578125000,30517578125,95214843750,164794921875,512695312500,885009765625,2746582031250
%N A187275 a(n) = (n/4)*5^(n/2)*((1+sqrt(5))^2+(-1)^n*(1-sqrt(5))^2).
%H A187275 G. C. Greubel, <a href="/A187275/b187275.txt">Table of n, a(n) for n = 0..1000</a>
%H A187275 R. Kemp, <a href="http://dx.doi.org/10.1016/0012-365X(82)90123-6">On the number of words in the language {w in Sigma* | w = w^R }^2</a>, Discrete Math., 40 (1982), 225-234. See Lemma 1.
%H A187275 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,10,0,-25).
%F A187275 a(n) = 10*a(n-2) - 25*a(n-4). - _Colin Barker_, Jul 25 2013
%F A187275 G.f.: 5*x*(x+1)*(5*x+1) / (5*x^2-1)^2. - _Colin Barker_, Jul 25 2013
%F A187275 a(2*n) = 6*n*5^n, a(2*n+1) = (2*n+1)*5^(n+1). - _Andrew Howroyd_, Mar 28 2016
%p A187275 See A187272.
%t A187275 LinearRecurrence[{0, 10, 0, -25}, {0, 5, 30, 75}, 30] (* _Vincenzo Librandi_, Mar 29 2016 *)
%o A187275 (Magma) /* By definition: */ Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); [Integers()!((n/4)*r^n*((1+r)^2+(-1)^n*(1-r)^2)): n in [0..30]]; // _Bruno Berselli_, Mar 29 2016
%o A187275 (Magma) I:=[0,5,30,75]; [n le 4 select I[n] else 10*Self(n-2)-25*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Mar 29 2016
%o A187275 (Python)
%o A187275 def A187275(n): return n*5**(1+(n>>1)) if n&1 else 3*n*5**(n>>1) # _Chai Wah Wu_, Feb 19 2024
%K A187275 nonn,easy
%O A187275 0,2
%A A187275 _N. J. A. Sloane_, Mar 07 2011