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Search: id:A005323
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| A005323 |
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Column of Motzkin triangle.
(Formerly M3480)
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+0
7
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| 1, 4, 14, 44, 133, 392, 1140, 3288, 9438, 27016, 77220, 220584, 630084, 1800384, 5147328, 14727168, 42171849, 120870324, 346757334, 995742748, 2862099185, 8234447672, 23713180780, 68350541480, 197188167735, 569371325796
(list; graph; listen)
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OFFSET
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3,2
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REFERENCES
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R. Donaghey and L. W. Shapiro, Motzkin numbers, J. Combin. Theory, Series A, 23 (1977), 291-301.
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FORMULA
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a(n) = number of (s(0), s(1), ..., s(n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| <= 1 for i = 1, 2, ..., n, s(0) = 0, s(n) = 3.
G.f.: z^3*M^4, where M is g.f. of Motzkin numbers (A001006).
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CROSSREFS
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Cf. A026300.
A diagonal of triangle A020474.
Sequence in context: A006645 A094309 A000300 this_sequence A027831 A097894 A065835
Adjacent sequences: A005320 A005321 A005322 this_sequence A005324 A005325 A005326
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003
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