

A097887


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.).


0



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, 240, 153, 84, 9, 919, 658, 351, 214, 45, 1, 2443, 1782, 891, 506, 165, 11, 6559, 4792, 2397, 1196, 500, 66, 1, 17759, 12896, 6565, 2964, 1352, 286, 13, 48417, 34892, 17993, 7765
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OFFSET

0,6


COMMENTS

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


LINKS

Table of n, a(n) for n=0..59.


FORMULA

G.f.=G=G(t, z) satisfies z^2*(24z+3z^2t+2tz3tz^2+t^2*z^2)G^2(1z)(12z+3z^22tz^2)G+(1z)^2=0.


EXAMPLE

Triangle begins:
1;
1;
1,1;
1,3;
2,6,1;
6,10,5;
18,17,15,1;
Row n contains 1+floor(n/2) terms.
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).


CROSSREFS

Cf. A001006, A089380.
Sequence in context: A016460 A248645 A161826 * A019761 A188614 A290798
Adjacent sequences: A097884 A097885 A097886 * A097888 A097889 A097890


KEYWORD

nonn,tabf


AUTHOR

Emeric Deutsch, Sep 02 2004


STATUS

approved



