%I #4 Mar 30 2012 17:35:59
%S 1,1,2,4,8,1,16,5,32,18,1,64,56,7,128,160,34,1,256,432,138,9,512,1120,
%T 500,55,1,1024,2816,1672,275,11,2048,6912,5264,1205,81,1,4096,16640,
%U 15808,4797,481,13,8192,39424,45696,17738,2471,112,1,16384,92160,128000
%N Triangle read by rows: T(n,k) is the number of Motzkin paths of length n having k high humps. (A hump is an upstep followed by 0 or more flatsteps followed by a downstep. A high hump is a hump that starts at a level higher than zero.).
%C Row sums are the Motzkin numbers (A001006).
%F G.f.=G=G(t, z) satisfies tz^2*(1-z)G^2-(1-2*z+tz^2)*G+1-z=0.
%e Triangle begins:
%e 1;
%e 1;
%e 2;
%e 4;
%e 8,1;
%e 16,5;
%e 32,18,1;
%e Row n contains floor(n/2) terms.
%e T(5,1)=5 counts HU(UD)D, U(UD)DH, UH(UD)D, U(UD)HD and U(UHD)D, where U=(1,1), H=(1,0), D=(1,-1) (the high humps are shown between parentheses).
%Y Cf. A001006.
%K nonn,tabf
%O 0,3
%A _Emeric Deutsch_, Sep 02 2004