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A190168 Number of peakless Motzkin paths of length n having no (1,0)-steps at levels 1,3,5,... . 3
1, 1, 1, 1, 1, 2, 4, 7, 12, 21, 38, 70, 130, 243, 457, 865, 1647, 3152, 6059, 11693, 22647, 44007, 85770, 167626, 328430, 644993, 1269413, 2503339, 4945897, 9788700, 19404866, 38526335, 76599502, 152503123, 304006284, 606745700, 1212335896, 2424964327, 4855454654 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

a(n) = A190167(n,0).

LINKS

Matthew House, Table of n, a(n) for n = 0..3142

FORMULA

G.f. G=G(z) satisfies the equation z^2*(1-z+z^2)G^2-(1+z^2)(1-z+z^2)G +1+z^2=0.

G.f.: (1+1/x^2-sqrt(1+1/x^4-2/x^2-4/x-(4-4*x)/(1-x+x^2)))/2. - Matthew House, Feb 12 2017

EXAMPLE

a(5)=2 because we have hhhhh and uuhdd, where u=(1,1), h=(1,0), d=(1,-1).

MAPLE

eq := z^2*(1-z+z^2)*G^2-(1+z^2)*(1-z+z^2)*G+1+z^2=0: g:=RootOf(eq, G): Gser:=series(g, z=0, 46): seq(coeff(Gser, z, n), n=0..38);

MATHEMATICA

CoefficientList[Series[(1 + 1/x^2 - Sqrt[1 + 1/x^4 - 2/x^2 - 4/x - (4 - 4 x)/(1 - x + x^2)])/2, {x, 0, 38}], x] (* Michael De Vlieger, Feb 12 2017 *)

CROSSREFS

Cf. A190167, A190165

Sequence in context: A000709 A054161 A023433 * A288133 A005126 A054151

Adjacent sequences:  A190165 A190166 A190167 * A190169 A190170 A190171

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 06 2011

STATUS

approved

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Last modified September 23 02:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)