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A104544 Triangle read by rows: T(n,k) is the number of Motzkin paths of length n having k HH's, where H=(1,0).

%I A104544 #4 Mar 30 2012 17:36:01
%S A104544 1,1,1,3,0,1,5,3,0,1,11,6,3,0,1,25,13,9,3,0,1,55,40,16,12,3,0,1,129,
%T A104544 95,60,20,15,3,0,1,303,250,155,80,25,18,3,0,1,721,661,415,235,100,31,
%U A104544 21,3,0,1,1743,1708,1206,620,335,120,38,24,3,0,1,4241,4515,3262,1946,875,455
%N A104544 Triangle read by rows: T(n,k) is the number of Motzkin paths of length n having k HH's, where H=(1,0).
%F A104544 G.f.=G=G(t, z) satisfies z^2(1+z-tz)G^2-(1-tz)G+1+z-tz=0.
%e A104544 Triangle starts:
%e A104544 1;
%e A104544 1,1;
%e A104544 3,0,1;
%e A104544 5,3,0,1;
%e A104544 11,6,3,0,1;
%e A104544 T(4,1)=3 because we have HHUD, UDHH and UHHD, where U=(1,1), D=(1,-1) and H=(1,0).
%Y A104544 Column 0 yields A104545. Row sums yield the Motzkin numbers (A001006).
%K A104544 nonn,tabl
%O A104544 1,4
%A A104544 _Emeric Deutsch_, Mar 14 2005