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 A257516 #8 Apr 29 2015 06:35:12
%S A257516 1,0,1,0,2,1,5,4,15,15,48,57,162,218,570,842,2070,3284,7709,12922,
%T A257516 29299,51255,113220,204781,443574,823554,1757947,3331818,7035054,
%U A257516 13552699,28387680,55401396,115369417,227501256,471780468,938107057,1939727280,3883120002
%N A257516 Number of 3-generalized Motzkin paths of length n with no level steps H=(3,0) at even level.
%F A257516 G.f.: (1-x^3-sqrt((1-x^3)*(1-4*x^2-x^3)))/(2*x^2).
%e A257516 For n=6 we have 5 paths: UDUDUD, UUDDUD, UDUUDD, UUUDDD and UUDUDD
%t A257516 CoefficientList[Series[(1-x^3-Sqrt[(1-x^3)*(1-4*x^2-x^3)])/(2*x^2), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 27 2015 *)
%Y A257516 Cf. A002212, A090345.
%K A257516 nonn
%O A257516 0,5
%A A257516 _José Luis Ramírez Ramírez_, Apr 27 2015