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 A134465 #33 Mar 26 2022 04:14:19
%S A134465 1,6,16,32,55,86,126,176,237,310,396,496,611,742,890,1056,1241,1446,
%T A134465 1672,1920,2191,2486,2806,3152,3525,3926,4356,4816,5307,5830,6386,
%U A134465 6976,7601,8262,8960,9696,10471,11286,12142,13040,13981,14966
%N A134465 Row sums of triangle A134464.
%C A134465 a(n) is the number of compositions of n+9 into n parts avoiding parts 2 and 3. - _Milan Janjic_, Jan 07 2016
%H A134465 Vincenzo Librandi, <a href="/A134465/b134465.txt">Table of n, a(n) for n = 1..1000</a>
%H A134465 David Anderson, E. S. Egge, M. Riehl, L. Ryan, R. Steinke, Y. Vaughan, <a href="http://arxiv.org/abs/1605.06825">Pattern Avoiding Linear Extensions of Rectangular Posets</a>, arXiv:1605.06825 [math.CO], 2016.
%H A134465 Colin Defant, <a href="https://arxiv.org/abs/1905.02309">Proofs of Conjectures about Pattern-Avoiding Linear Extensions</a>, arXiv:1905.02309 [math.CO], 2019.
%H A134465 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A134465 Binomial transform of [1, 5, 5, 1, 0, 0, 0, ...].
%F A134465 G.f.: x*(1+2*x-2*x^2) / (1-x)^4. - _R. J. Mathar_, Apr 04 2012
%F A134465 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 29 2012
%e A134465 a(4) = 32 = sum of row 4, triangle A134464: (4 + 6 + 9 + 13).
%e A134465 a(4) = 32 = (1, 3, 3, 1) dot (1, 5, 5, 1) = (1 + 15 + 15 + 1).
%t A134465 CoefficientList[Series[(1+2*x-2*x^2)/(1-x)^4,{x,0,50}],x] (* _Vincenzo Librandi_, Jun 29 2012 *)
%o A134465 (Magma) I:=[1, 6, 16, 32]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jun 29 2012
%o A134465 (PARI) Vec(x*(1+2*x-2*x^2)/(1-x)^4 + O(x^50)) \\ _Altug Alkan_, Jan 07 2016
%o A134465 (Sage) ((1+2*x-2*x^2)/(1-x)^4).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, May 08 2019
%o A134465 (GAP) a:=[1,6,16,32];; for n in [5..50] do a[n]:=4*a[n-1]-6*a[n-2]+ 4*a[n-3]-a[n-4]; od; a; # _G. C. Greubel_, May 08 2019
%Y A134465 Cf. A134464.
%K A134465 nonn,easy
%O A134465 1,2
%A A134465 _Gary W. Adamson_, Oct 26 2007