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A190166 Number of (1,0)-steps at levels 0,2,4,... in all peakless Motzkin paths of length n. 2
0, 1, 2, 3, 6, 14, 34, 83, 202, 495, 1224, 3046, 7616, 19115, 48130, 121527, 307602, 780244, 1982834, 5047377, 12867438, 32847357, 83952780, 214806750, 550170300, 1410412561, 3618785462, 9292203549, 23877482490, 61397367692, 157972743178, 406693829059, 1047585820586, 2699811117189 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)=Sum(k*A190164(n,k),k>=0).

a(n)=A110236(n) - A190169(n).

LINKS

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

FORMULA

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

Conjecture: (-n+1)*a(n) +(3*n-4)*a(n-1) +2*(-n+1)*a(n-2) +3*(n-2)*a(n-3) +2*(-n+3)*a(n-4) +(3*n-8)*a(n-5) +(-n+3)*a(n-6)=0. - R. J. Mathar, Apr 09 2019

EXAMPLE

a(4)=6 because in h'h'h'h', h'uhd, uhdh', and uhhd, where u=(1,1), h=(1,0), d=(1,-1), we have 4+1+1+0 h-steps at even levels (marked).

MAPLE

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

CROSSREFS

Cf. A190164, A110236, A190169, A004148

Sequence in context: A291401 A331875 A010357 * A238823 A002995 A093467

Adjacent sequences:  A190163 A190164 A190165 * A190167 A190168 A190169

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 06 2011

STATUS

approved

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)