%I A050253
%S A050253 1,1,1,2,3,5,9,16,29,54,101,191,365,702,1359,2647,5181,10187,20113,
%T A050253 39856,79243,158036,316053,633689,1273559,2565136,5177043,10468199,
%U A050253 21204379,43022215,87423573,177906552,362531425,739700055,1511091377
%N A050253 G.f.: ( 1 - x^2 - Sqrt[ 1 - 2 x^2 - 4 x^3 - 3 x^4 ] ) / ( 2 x^3 ).
%C A050253 a(n)=number of Motzkin (n-1)-paths (A001006) containing no three consecutive 
               weakly-rising steps (n>=1). A weakly-rising step is an upstep or 
               flatstep. For example, a(5)=5 counts FUDF, UDFF, UDUD, UFDF, UUDD 
               while the path FUFD, say, is not counted because the first 3 steps 
               are weakly-rising. - David Callan (callan(AT)stat.wisc.edu), Oct 
               25 2004
%F A050253 a(n)=A108296(n+2)-A108296(n). - Paul Barry (pbarry(AT)wit.ie), May 31 
               2005
%F A050253 G.f.: 1/(1-x-x^3/(1-x^2-x^3/(1-x-x^3/(1-x^2-x^3/(1-x-x^3/(1-... (continued 
               fraction). [From Paul Barry (pbarry(AT)wit.ie), May 25 2009]
%Y A050253 Sequence in context: A103285 A000049 A000050 this_sequence A107250 A050168 
               A072176
%Y A050253 Adjacent sequences: A050250 A050251 A050252 this_sequence A050254 A050255 
               A050256
%K A050253 easy,nonn
%O A050253 0,4
%A A050253 Emanuele Munarini (munarini(AT)mate.polimi.it), May 09 2003