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 A123887 #25 Sep 08 2022 08:45:28 %S A123887 1,6,36,210,1230,7200,42150,246750,1444500,8456250,49503750,289800000, %T A123887 1696518750,9931593750,58140562500,340360781250,1992506718750, %U A123887 11664337500000,68284221093750,399742792968750,2340135070312500,13699389316406250,80197621933593750,469485056250000000 %N A123887 Expansion of g.f.: (1+x+x^2)/(1-5*x-5*x^2). %H A123887 G. C. Greubel, <a href="/A123887/b123887.txt">Table of n, a(n) for n = 0..1000</a> %H A123887 A. Burstein and T. Mansour, <a href="https://arxiv.org/abs/math/0112281">Words restricted by 3-letter ...</a>, arXiv:math/0112281 [math.CO], 2001. %H A123887 A. Burstein and T. Mansour, <a href="https://doi.org/10.1007/s000260300000">Words Restricted by 3-Letter Generalized Multipermutation Patterns</a>, Annals. Combin., 7 (2003), 1-14. %H A123887 Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, <a href="https://www.emis.de/journals/JIS/VOL18/Szczyrba/sz3.html">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5. %H A123887 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,5). %F A123887 a(0)=1, a(1)=6, a(2)=36, a(n) = 5*a(n-1) + 5*a(n-2) for n>2. - _Philippe Deléham_, Sep 19 2009 %p A123887 seq(coeff(series((1+x+x^2)/(1-5*x-5*x^2), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Aug 07 2019 %t A123887 CoefficientList[Series[(1+x+x^2)/(1-5x-5x^2),{x,0,30}],x] (* or *) LinearRecurrence[{5,5},{1,6,36}, 40] (* _Harvey P. Dale_, Jan 03 2019 *) %o A123887 (PARI) my(x='x+O('x^30)); Vec((1+x+x^2)/(1-5*x-5*x^2)) \\ _G. C. Greubel_, Aug 07 2019 %o A123887 (Magma) I:=[6,36]; [1] cat [n le 2 select I[n] else 5*(Self(n-1)+ Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Aug 07 2019 %o A123887 (Sage) %o A123887 def A123887_list(prec): %o A123887 P.<x> = PowerSeriesRing(ZZ, prec) %o A123887 return P( (1+x+x^2)/(1-5*x-5*x^2) ).list() %o A123887 A123887_list(30) # _G. C. Greubel_, Aug 07 2019 %o A123887 (GAP) a:=[6,36];; for n in [3..30] do a[n]:=5*(a[n-1]+a[n-2]); od; Concatenation([1], a); # _G. C. Greubel_, Aug 07 2019 %Y A123887 Column 6 in A265584. %K A123887 nonn,easy %O A123887 0,2 %A A123887 _N. J. A. Sloane_, Nov 20 2006