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 A192369 #25 Apr 24 2025 02:13:30 %S A192369 1,2,15,90,617,4248,29945,213404,1535661,11129314,81123369,594092166, %T A192369 4367701295,32216566492,238301617605,1766979857196,13129849298327, %U A192369 97746629874786,728897653778335,5443488765350770,40706993579981847,304779612155116444,2284440756129389775,17139937071103287600 %N A192369 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (0,2), (1,0), (2,0), and (2,2). %C A192369 Diagonal of the rational function 1 / (1 - x - y - x^2 - y^2 - (x*y)^2). - _Ilya Gutkovskiy_, Apr 23 2025 %F A192369 G.f. is a nested square root, see Maple program. - _Mark van Hoeij_, Apr 16 2013 %p A192369 p4 := (x-1)*(x^3+5*x^2+7*x-1); %p A192369 ogf := sqrt(((2*x^2+4*x-3)/p4-2/sqrt(p4))/(4*x^2-8*x-5)); %p A192369 series(ogf, x=0, 30); # _Mark van Hoeij_, Apr 16 2013 %o A192369 (PARI) /* same as in A092566 but use */ %o A192369 steps=[[0,1], [0,2], [1,0], [2,0], [2,2]]; %o A192369 /* _Joerg Arndt_, Jun 30 2011 */ %K A192369 nonn %O A192369 0,2 %A A192369 _Eric Werley_, Jun 29 2011 %E A192369 Terms > 81123369 from _Joerg Arndt_, Jun 30 2011