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Search: id:A122868
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| A122868 |
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Expansion of 1/sqrt(1-6x-3x^2). |
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+0
1
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| 1, 3, 15, 81, 459, 2673, 15849, 95175, 576963, 3523257, 21640365, 133549155, 827418645, 5143397535, 32063180535, 200367960201, 1254816463923, 7873205412825, 49482344889261, 311457546052659
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A084609. Central coefficients of (1+3x+3x^2)^n.
The number of free (3,3)-Motzkin paths of length n, where free (k,t)-Motzkin paths are the free Motzkin paths with level steps of weight k and down steps of weight t. For example a(2)=15 because there are 9, 3, 3 paths consisting of two level steps, UD's and DU's, respectively. - Carol J. Wang (cerlined7(AT)hotmail.com), Nov 27 2007
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REFERENCES
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W. Y. C. Chen, N. Y. Li, L. W. Shapiro and S. H. F. Yan, Matrix identities on weighted partial Motzkin paths, European J. Combinatorics, 28(2007)1196--2007.
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FORMULA
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a(n)=sum{k=0..floor(n/2), C(n,2k)*C(2k,k)*3^(n-k)}.
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CROSSREFS
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Sequence in context: A003448 A084120 A163470 this_sequence A015680 A084208 A059271
Adjacent sequences: A122865 A122866 A122867 this_sequence A122869 A122870 A122871
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 16 2006
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