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 A099524 #23 Jan 20 2024 17:05:21
%S A099524 1,5,25,126,635,3200,16126,81265,409525,2063751,10400020,52409625,
%T A099524 264111876,1330959400,6707206625,33800145001,170331684405,
%U A099524 858365628650,4325628288251,21798473125660,109850731256950,553579284573001
%N A099524 Expansion of 1/(1-5*x-x^3).
%C A099524 A transform of A000351 under the mapping mapping g(x)->(1/(1-x^3))g(x/(1-x^3)).
%C A099524 a(n) equals the number of n-length words on {0,1,2,3,4,5} such that 0 appears only in a run which length is a multiple of 3. - _Milan Janjic_, Feb 17 2015
%H A099524 Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Janjic/janjic73.html">Binomial Coefficients and Enumeration of Restricted Words</a>, Journal of Integer Sequences, 2016, Vol 19, #16.7.3
%H A099524 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,1).
%F A099524 a(n) = 5*a(n-1) + a(n-3).
%F A099524 a(n) = Sum_(k=0..floor(n/3)) binomial(n-2*k, k)*5^(n-3*k).
%t A099524 CoefficientList[Series[1/(1-5x-x^3),{x,0,30}],x] (* or *) LinearRecurrence[ {5,0,1},{1,5,25},30] (* _Harvey P. Dale_, May 08 2012 *)
%Y A099524 Cf. A000351, A099504.
%K A099524 nonn,easy
%O A099524 0,2
%A A099524 _Paul Barry_, Oct 20 2004