A097887 - OEIS

%I #3 Mar 30 2012 17:35:59

%S 1,1,1,1,1,3,2,6,1,6,10,5,18,17,15,1,50,35,35,7,133,88,73,28,1,349,

%T 240,153,84,9,919,658,351,214,45,1,2443,1782,891,506,165,11,6559,4792,

%U 2397,1196,500,66,1,17759,12896,6565,2964,1352,286,13,48417,34892,17993,7765

%N Triangle read by rows: T(n,k) is the number of Motzkin paths of length n having k low humps. (A hump is an upstep followed by 0 or more flatsteps followed by a downstep. A low hump is a hump that starts at level zero.).

%C Row sums are the Motzkin numbers (A001006). Column 0 gives A089380.

%F G.f.=G=G(t, z) satisfies z^2*(2-4z+3z^2-t+2tz-3tz^2+t^2*z^2)G^2-(1-z)(1-2z+3z^2-2tz^2)G+(1-z)^2=0.

%e Triangle begins:

%e 1;

%e 1;

%e 1,1;

%e 1,3;

%e 2,6,1;

%e 6,10,5;

%e 18,17,15,1;

%e Row n contains 1+floor(n/2) terms.

%e T(5,2)=5 counts (UD)(UHD), (UHD)(UD), H(UD)(UD), (UD)H(UD) and (UD)(UD)H, where U=(1,1), H=(1,0), D=(1,-1) (the low humps are shown between parentheses).

%Y Cf. A001006, A089380.

%K nonn,tabf

%O 0,6

%A _Emeric Deutsch_, Sep 02 2004