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 A124820 #32 Aug 03 2016 11:30:16
%S A124820 1,3,9,28,88,277,872,2745,8641,27201,85626,269542,848491,2670964,
%T A124820 8407925,26467299,83316385,262271568,825604416,2598919345,8181135700,
%U A124820 25753389181,81069068969,255197244033,803335158406,2528817970494
%N A124820 Expansion of (1-x)/(1-4*x+3*x^2-x^3).
%C A124820 Row sums of A124819.
%C A124820 Let M = a triangle with the triangular series in every column, but the leftmost column is shifted upwards one row. Then A124820 = Lim_{n->inf} M^n, the left-shifted vector considered as a sequence. - _Gary W. Adamson_, Jul 27 2010
%C A124820 Second trisection of Narayana's cows sequence A000930. - _Oboifeng Dira_, Aug 03 2016
%H A124820 Vincenzo Librandi, <a href="/A124820/b124820.txt">Table of n, a(n) for n = 0..1000</a>
%H A124820 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,1).
%F A124820 a(n) = sum( k=0..n, C(n+2k+1, 3k+1) ).
%F A124820 a(n) = A052529(n+1) - A052529(n), n>1. - _R. J. Mathar_, Dec 15 2008
%t A124820 CoefficientList[Series[(1 - x)/(1 - 4 x + 3 x^2 - x^3), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jun 20 2014 *)
%t A124820 LinearRecurrence[{4,-3,1},{1,3,9},30] (* _Harvey P. Dale_, Apr 29 2016 *)
%t A124820 Table[Sum[Binomial[n + 2 k + 1, 3 k + 1], {k, 0, n}], {n, 0, 25}] (* _Michael De Vlieger_, Aug 03 2016 *)
%o A124820 (PARI) a(n)=([0,1,0; 0,0,1; 1,-3,4]^n*[1;3;9])[1,1] \\ _Charles R Greathouse IV_, Aug 03 2016
%K A124820 nonn,easy
%O A124820 0,2
%A A124820 _Paul Barry_, Nov 08 2006