The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A114464

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A114464

Number of Dyck paths of semilength n having no ascents of length 2 that start at an even level.
(history; published version)

#12 by Joerg Arndt at Sat Feb 15 02:31:27 EST 2014

STATUS

proposed

approved

#11 by Vincenzo Librandi at Sat Feb 15 01:43:58 EST 2014

STATUS

editing

proposed

#10 by Vincenzo Librandi at Sat Feb 15 01:43:48 EST 2014

LINKS

Vincenzo Librandi, <a href="/A114464/b114464.txt">Table of n, a(n) for n = 0..200</a>

STATUS

approved

editing

#9 by Vaclav Kotesovec at Thu Feb 13 04:03:05 EST 2014

STATUS

editing

approved

#8 by Vaclav Kotesovec at Thu Feb 13 04:02:01 EST 2014

FORMULA

Recurrence: (n-3)*(n+1)*a(n) = (4*n^2 - 14*n + 9)*a(n-1) - (2*n^2 - 10*n + 15)*a(n-2) + (4*n^2 - 26*n + 39)*a(n-3) - (n-6)*(n-2)*a(n-4). - Vaclav Kotesovec, Feb 13 2014

a(n) ~ sqrt(2*sqrt(3)-3) * (2+sqrt(3))^n / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 13 2014

#7 by Vaclav Kotesovec at Thu Feb 13 03:55:52 EST 2014

MATHEMATICA

CoefficientList[Series[(1-x+3*x^2-x^3-(1-x)*Sqrt[(1-4*x+x^2)*(1+x^2)])/2/x, {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 13 2014 *)

STATUS

approved

editing

#6 by R. J. Mathar at Mon Nov 26 15:05:36 EST 2012

STATUS

editing

approved

#5 by R. J. Mathar at Mon Nov 26 14:21:20 EST 2012

FORMULA

Conjecture: (n+1)*a(n) +(-5*n+3)*a(n-1) +2*(3*n-7)*a(n-2) +2*(-3*n+11)*a(n-3) +(5*n-27)*a(n-4) +(-n+7)*a(n-5)=0. - R. J. Mathar, Nov 26 2012

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 18:59:13 EDT 2012

FORMULA

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

Discussion

Fri Mar 30

18:59

OEIS Server: https://oeis.org/edit/global/287

#3 by Russ Cox at Fri Mar 30 17:36:07 EDT 2012

AUTHOR

_Emeric Deutsch (deutsch(AT)duke.poly.edu), _, Nov 29 2005

Discussion

Fri Mar 30

17:36

OEIS Server: https://oeis.org/edit/global/173