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Search: id:A129166
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| A129166 |
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Number of skew Dyck paths of semilength n with no base pyramids. A skew Dyck path is a path in the first quadrant which begins at the origin, ends on the x-axis, consists of steps U=(1,1)(up), D=(1,-1)(down) and L=(-1,-1)(left) so that up and left steps do not overlap. The length of the path is defined to be the number of its steps. A pyramid in a skew Dyck word (path) is a factor of the form u^h d^h, h being the height of the pyramid. A base pyramid is a pyramid starting on the x-axis. |
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+0
2
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| 1, 0, 1, 5, 19, 73, 292, 1203, 5065, 21697, 94274, 414514, 1840981, 8247011, 37220261, 169079113, 772489020, 3547371679, 16364309243, 75799327800, 352402156770, 1643878188646, 7691841654538, 36091803172733
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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a(n)=A129165(n,0).
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REFERENCES
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E. Deutsch, E. Munarini and S. Rinaldi, Skew Dyck paths (in preparation).
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FORMULA
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G.f.=(1-z)[3-3z-sqrt(1-6z+5z^2)]/[2-(1-z)[1-z-sqrt(1-6z+5z^2)]].
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EXAMPLE
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a(2)=1 because we have UUDL.
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MAPLE
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G:=(1-z)*(3-3*z-sqrt(1-6*z+5*z^2))/(2-(1-z)*(1-z-sqrt(1-6*z+5*z^2))): Gser:=series(G, z=0, 30): seq(coeff(Gser, z, n), n=0..27);
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CROSSREFS
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Cf. A129165.
Sequence in context: A086386 A047155 A034548 this_sequence A149763 A149764 A149765
Adjacent sequences: A129163 A129164 A129165 this_sequence A129167 A129168 A129169
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2007
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