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Search: id:A097888
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| A097888 |
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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.). |
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+0
1
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| 1, 1, 2, 4, 8, 1, 16, 5, 32, 18, 1, 64, 56, 7, 128, 160, 34, 1, 256, 432, 138, 9, 512, 1120, 500, 55, 1, 1024, 2816, 1672, 275, 11, 2048, 6912, 5264, 1205, 81, 1, 4096, 16640, 15808, 4797, 481, 13, 8192, 39424, 45696, 17738, 2471, 112, 1, 16384, 92160, 128000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums are the Motzkin numbers (A001006).
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FORMULA
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G.f.=G=G(t, z) satisfies tz^2*(1-z)G^2-(1-2*z+tz^2)*G+1-z=0.
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EXAMPLE
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Triangle begins:
1;
1;
2;
4;
8,1;
16,5;
32,18,1;
Row n contains floor(n/2) terms.
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).
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CROSSREFS
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Cf. A001006.
Adjacent sequences: A097885 A097886 A097887 this_sequence A097889 A097890 A097891
Sequence in context: A100880 A102256 A000455 this_sequence A030275 A097874 A097885
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 02 2004
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