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 A191678 #17 Apr 17 2013 15:58:50 %S A191678 1,1,5,15,62,233,937,3729,15121,61492,251942,1036215,4279754,17731181, %T A191678 73670725,306823695,1280574706,5354602495,22426876445,94070238840, %U A191678 395106054632,1661489413472,6994494531010,29474635716345,124319047552309,524797934104312,2217091297558466,9373180869094923 %N A191678 Number of lattice paths from (0,0) to (n,n) using steps (1,0), (1,1), (0,2), (2,2). %F A191678 G.f.: A(x) where (4*x^6+12*x^5-20*x^3+27*x^2+12*x-4)*A(x)^3-(3*x^2+3*x-3)*A(x)+1 = 0. - _Mark van Hoeij_, Apr 17 2013 %p A191678 P := (4*x^6+12*x^5-20*x^3+27*x^2+12*x-4)*A^3-(3*x^2+3*x-3)*A+1; %p A191678 Q := eval(P, A=A+1): %p A191678 series(RootOf(Q,A)+1, x=0, 30); # _Mark van Hoeij_, Apr 17 2013 %o A191678 (PARI) /* same as in A092566 but use */ %o A191678 steps=[[1,0], [1,1], [0,2], [2,2]]; %o A191678 /* Joerg Arndt, Jun 30 2011 */ %Y A191678 Cf. A001850, A026641, A036355, A137644, A192364, A192365, A192369, A191354. %K A191678 nonn %O A191678 0,3 %A A191678 _Joerg Arndt_, Jun 30 2011