login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A190169 Number of (1,0)-steps at levels 1,3,5,... in all peakless Motzkin paths of length n. 2
0, 0, 0, 1, 4, 10, 24, 60, 152, 386, 980, 2488, 6324, 16098, 41032, 104711, 267512, 684138, 1751316, 4487217, 11506792, 29530524, 75841152, 194910254, 501234960, 1289755668, 3320603016, 8553723949, 22044934324, 56841474482, 146626826376, 378392593206, 976884539336, 2522936490418 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n)=Sum(k*A190167(n,k),k>=0).

a(n)=A110236(n) - A190166(n).

LINKS

Table of n, a(n) for n=0..33.

FORMULA

G.f. = (1-2z+z^2-2z^3+z^4)/[2z(1-z+z^2)sqrt((1+z+z^2)(1-3z+z^2))]-1/(2z).

Conjecture: -(n-1)*(n+1)*a(n) -n*(n-19)*a(n-1) +2*(n-1)*(7*n-40)*a(n-2) -(n-2)*(17*n-97)*a(n-3) +2*(9*n^2-64*n+119)*a(n-4) -17*(n-4)*(n-5)*a(n-5) +(19*n-59)*(n-5)*a(n-6) -2*(8*n-21)*(n-6)*a(n-7) +2*(2*n-5)*(n-7)*a(n-8)=0. - R. J. Mathar, Apr 09 2019

EXAMPLE

a(4)=4 because in hhhh, huh'd, uh'dh, and uh'h'd, where u=(1,1), h=(1,0), d=(1,-1), we have 0+1+1+2 h-steps at odd levels (marked).

MAPLE

G := ((1-2*z+z^2-2*z^3+z^4)*1/2)/(z*(1-z+z^2)*sqrt((1+z+z^2)*(1-3*z+z^2)))-(1/2)/z: Gser:=series(G, z=0, 36): seq(coeff(Gser, z, n), n=0..33);

CROSSREFS

Cf. A190167, A110236, A190166

Sequence in context: A080628 A225127 A230954 * A212330 A291412 A001868

Adjacent sequences:  A190166 A190167 A190168 * A190170 A190171 A190172

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 06 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 25 20:01 EDT 2021. Contains 347659 sequences. (Running on oeis4.)