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Search: id:A097892
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| A097892 |
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Triangle read by rows: T(n,k) is the number of Motzkin paths of length n and having k peaks at even height. |
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+0
1
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| 1, 1, 2, 4, 8, 1, 17, 4, 38, 12, 1, 88, 34, 5, 209, 95, 18, 1, 506, 264, 59, 6, 1244, 731, 187, 25, 1, 3097, 2020, 582, 92, 7, 7791, 5578, 1786, 322, 33, 1, 19773, 15404, 5420, 1096, 134, 8, 50563, 42558, 16308, 3652, 510, 42, 1, 130149, 117652, 48744, 11960, 1872
(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 z^2*(1-z)G^2-(1-z)(1-z+z^2-tz^2)G+1-z+z^2-tz^2=0.
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EXAMPLE
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Triangle begins:
1;
1;
2;
4;
8,1;
17,4;
38,12,1;
Row n (n>=2) contains floor(n/2) terms.
T(5,1)=4 counts HU(UD)D, U(UD)DH, UH(UD)D and U(UD)HD, where U=(1,1), H=(1,0), D=(1,-1) (the peaks at even height are shown between parentheses).
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CROSSREFS
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Cf. A001006.
Sequence in context: A030275 A097874 A097885 this_sequence A033921 A167420 A076232
Adjacent sequences: A097889 A097890 A097891 this_sequence A097893 A097894 A097895
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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 03 2004
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