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 A099504 #17 Aug 04 2023 01:43:29
%S A099504 1,5,25,124,615,3050,15126,75015,372025,1844999,9149980,45377875,
%T A099504 225044376,1116071900,5534981625,27449863749,136133246845,
%U A099504 675131252600,3348206399251,16604898749410,82349362494450,408398606072999
%N A099504 Expansion of 1/(1-5*x+x^3).
%C A099504 A transform of A000351 under the mapping g(x)->(1/(1+x^3))g(x/(1+x^3)).
%H A099504 G. C. Greubel, <a href="/A099504/b099504.txt">Table of n, a(n) for n = 0..1000</a>
%H A099504 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,-1).
%F A099504 a(n) = 5*a(n-1) - a(n-3).
%F A099504 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k, k)*(-1)^k*5^(n-3*k).
%p A099504 A099504:=n->sum(binomial(n-2*i, i)*(-1)^i*5^(n-3*i), i=0..floor(n/3)); seq(A099504(n), n=0..30); # _Wesley Ivan Hurt_, Dec 03 2013
%t A099504 Table[Sum[Binomial[n-2*i,i]*(-1)^i*5^(n-3*i), {i,0,Floor[n/3]}], {n,0, 30}] (* _Wesley Ivan Hurt_, Dec 03 2013 *)
%t A099504 LinearRecurrence[{5,0,-1}, {1,5,25}, 30] (* _G. C. Greubel_, Aug 03 2023 *)
%o A099504 (Magma) [n le 3 select 5^(n-1) else 5*Self(n-1) -Self(n-3): n in [1..30]]; // _G. C. Greubel_, Aug 03 2023
%o A099504 (SageMath)
%o A099504 @CachedFunction
%o A099504 def a(n): # a = A099504
%o A099504 if (n<3): return 5^n
%o A099504 else: return 5*a(n-1) - a(n-3)
%o A099504 [a(n) for n in range(31)] # _G. C. Greubel_, Aug 03 2023
%Y A099504 Cf. A000071, A000351, A076264, A099503.
%K A099504 easy,nonn
%O A099504 0,2
%A A099504 _Paul Barry_, Oct 20 2004