The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A191398 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A191398

Number of dispersed Dyck paths of length n (i.e., Motzkin paths of length n with no (1,0)-steps at positive heights) having no DHU's (here U=(1,1), H=(1,0), and D=(1,-1)).
(history; published version)

#18 by Michel Marcus at Mon Mar 27 14:48:27 EDT 2017

STATUS

reviewed

approved

#17 by Joerg Arndt at Mon Mar 27 10:56:51 EDT 2017

STATUS

proposed

reviewed

#16 by Jon E. Schoenfield at Mon Mar 27 01:44:37 EDT 2017

STATUS

editing

proposed

#15 by Jon E. Schoenfield at Mon Mar 27 01:44:33 EDT 2017

NAME

Number of dispersed Dyck paths of length n (i.e. , Motzkin paths of length n with no (1,0)-steps at positive heights) having no DHU's (here U=(1,1), H=(1,0), and D=(1,-1)).

STATUS

proposed

editing

#14 by G. C. Greubel at Sun Mar 26 23:57:04 EDT 2017

STATUS

editing

proposed

#13 by G. C. Greubel at Sun Mar 26 23:56:55 EDT 2017

COMMENTS

a(n)=A191397(n,0).

STATUS

proposed

editing

#12 by G. C. Greubel at Sun Mar 26 23:55:46 EDT 2017

STATUS

editing

proposed

#11 by G. C. Greubel at Sun Mar 26 23:55:37 EDT 2017

LINKS

G. C. Greubel, <a href="/A191398/b191398.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

a(n) = A191397(n,0).

G.f.: g(z)=2/(1-z-2*z^3+(1-z)*sqrt(1-4*z^2)).

PROG

(PARI) x='x+O('x^50); Vec(2/(1-x-2*x^3+(1-x)*sqrt(1-4*x^2))) \\ G. C. Greubel, Mar 26 2017

STATUS

approved

editing

#10 by R. J. Mathar at Tue Jun 14 11:50:48 EDT 2016

STATUS

editing

approved

#9 by R. J. Mathar at Tue Jun 14 11:50:41 EDT 2016

FORMULA

Conjecture: -(n+2)*(n-3)*a(n) +2*(-23*n^2-3*n-14)*a(n-1) +2*(n^2-7*n+8)*a(n-2) +24*(7-3*n-^2+12*n-10)*a(n-3) +(7*n^2-1931*n+4638)*a(n-4) +(7*n-24)4*a(n-5) +4*(-n+1-2)^2*a(n-6) +4*(n-3)*a(n-7)=0. - R. J. Mathar, Jun 14 2016