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A114464
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Number of Dyck paths of semilength n having no ascents of length 2 that start at an even level.
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5
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1, 1, 1, 2, 6, 18, 54, 166, 522, 1670, 5418, 17786, 58974, 197226, 664494, 2253390, 7685394, 26345230, 90721362, 313682098, 1088609142, 3790610306, 13239554790, 46371693174, 162835695258, 573160873750, 2021885799162, 7146955776554
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Column 0 of A114462.
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FORMULA
| G.f.=[1-z+3z^2-z^3-(1-z)sqrt((1-4z+z^2)(1+z^2))]/(2z).
G.f. 1+x/(1-x)c(x^2/(1-x)^4), c(x) the g.f. of A000108; a(n+1)=sum{k=0..floor(n/2), C(n+2k,4k)C(k)}; - Paul Barry (pbarry(AT)wit.ie), May 31 2006
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EXAMPLE
| a(4)=6 because we have UDUDUDUD, UDUUUDDD, UUUDDDUD, UUUDUDDD, UUUDDUDD and UUUUDDDD, where U=(1,1), D=(1,-1).
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MAPLE
| G:=(1-z+3*z^2-z^3-(1-z)*sqrt((1-4*z+z^2)*(1+z^2)))/2/z: Gser:=series(G, z=0, 33): 1, seq(coeff(Gser, z^n), n=1..30);
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CROSSREFS
| Cf. A114462, A114463, A114465.
Sequence in context: A008776 A134635 A192338 * A062415 A086680 A148455
Adjacent sequences: A114461 A114462 A114463 * A114465 A114466 A114467
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 29 2005
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