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Search: id:A114465
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| A114465 |
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Number of Dyck paths of semilength n having no ascents of length 2 that start at an odd level. |
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+0
4
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| 1, 1, 2, 5, 13, 36, 105, 317, 982, 3105, 9981, 32520, 107157, 356481, 1195662, 4038909, 13728369, 46919812, 161143157, 555857157, 1924956954, 6689953057, 23325404153, 81567552320, 286009944649, 1005371062561, 3542175587306
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OFFSET
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0,3
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COMMENT
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Column 0 of A114463.
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FORMULA
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G.f.=[1-z^2-sqrt((1+z^2)(1-4z+z^2))]/[2z(1-z+z^2)].
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EXAMPLE
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a(4)=13 because among the 14 Dyck paths of semilength 4 only UUD(UU)DDD has an ascent of length 2 that starts at an odd level (shown between parentheses).
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MAPLE
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g:=-1/2/z/(1+z^2-z)*(z^2-1+sqrt((z^2+1)*(z^2-4*z+1))): gser:=series(g, z=0, 33): 1, seq(coeff(gser, z^n), n=1..30);
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CROSSREFS
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Cf. A114463, A114462, A114464.
Sequence in context: A136751 A087626 A125094 this_sequence A135310 A135337 A133365
Adjacent sequences: A114462 A114463 A114464 this_sequence A114466 A114467 A114468
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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), Nov 29 2005
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