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Search: id:A121320
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| A121320 |
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Number of vertices in all ordered (plane) trees with n edges that are at distance two from all the leaves above them. |
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+0
1
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| 0, 0, 1, 2, 6, 18, 59, 203, 724, 2643, 9802, 36755, 138935, 528406, 2019419, 7748125, 29825844, 115132729, 445498768, 1727434607, 6710501025, 26110567532, 101744332967, 396983837719, 1550777652546, 6064476854065, 23739056348161
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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G.f.: {z^2/(1 - z - z^2)]*(1/2)*(1 + 1/sqrt(1 - 4z))
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EXAMPLE
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a(4)=6 since the root has the distance two property for the trees uudduudd and uudududd. There are similar points at height 1 for uuududdd, uuudddud, and uduuuddd. The distance two point is at height 2 for uuuudddd.
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MATHEMATICA
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CoefficientList[Series[x^2(1 + 1/Sqrt[1 - 4x])/(2(1 - x - x^2)), {x, 0, 26}], x] - RGWV Aug 21 2006
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CROSSREFS
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Cf. A000045, A024718.
Sequence in context: A000137 A085139 A036675 this_sequence A002527 A005566 A005631
Adjacent sequences: A121317 A121318 A121319 this_sequence A121321 A121322 A121323
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KEYWORD
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easy,nonn
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AUTHOR
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Lou Shapiro (lshapiro(AT)howard.edu), Aug 25 2006
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EXTENSIONS
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More terms from RGWV Aug 21 2006
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