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%I #3 Mar 30 2012 17:35:59
%S 1,1,1,1,2,2,5,3,1,12,6,3,28,16,6,1,66,44,13,4,159,117,36,10,1,390,
%T 308,108,24,5,969,817,317,69,15,1,2432,2188,912,220,40,6,6157,5898,
%U 2616,698,120,21,1,15707,15968,7526,2164,401,62,7,40340,43381,21696,6638,1355
%N Triangle read by rows: T(n,k) is the number of Motzkin paths of length n and having k peaks at odd height.
%C Row sums are the Motzkin numbers (A001006).
%F G.f.=G=G(t, z) satisfies z^2*(1-z+z^2-tz^2)G^2-(1-z)(1-z+z^2-tz^2)G+1-z=0.
%e Triangle begins:
%e 1;
%e 1;
%e 1,1;
%e 2,2;
%e 5,3,1;
%e 12,6,3;
%e Row n has 1+floor(n/2) terms.
%e T(5,2)=3 counts H(UD)(UD), (UD)H(UD) and (UD)(UD)H, where U=(1,1), H=(1,0), D=(1,-1) (the peaks at odd height are shown between parentheses).
%Y Cf. A001006.
%K nonn,tabf
%O 0,5
%A _Emeric Deutsch_, Sep 03 2004
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