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Search: id:A109188
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| A109188 |
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Number of (1,0) steps in all Grand Motzkin paths of length n. (A Grand Motzkin path is a path in the half-plane x>=0, starting at (0,0), ending at (n,0) and consisting of steps u=(1,1), d=(1,-1) and h=(1,0).). |
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+0
3
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| 1, 2, 9, 28, 95, 306, 987, 3144, 9963, 31390, 98483, 307836, 959257, 2981174, 9243405, 28601712, 88342659, 272428758, 838903371, 2579937060, 7924966749, 24317716038, 74546117121, 228317474952, 698708409525, 2136597743826
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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G.f.=z(1-z)/(1-2z-3z^2)^(3/2).
a(n)=(n+1)*A002426(n). - Paul Barry (pbarry(AT)wit.ie), Apr 19 2008
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EXAMPLE
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a(3)=9 because we have the following 7 (=A002426(3)) Grand Motzkin paths of length 3: hhh, hud, hdu, udh, duh, uhd and dhu; they have a total of 9 h-steps.
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MAPLE
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g:=z*(1-z)/(1-2*z-3*z^2)^(3/2): gser:=series(g, z=0, 33): seq(coeff(gser, z^n), n=1..30);
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CROSSREFS
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Cf. A109187.
Sequence in context: A131066 A058877 A026087 this_sequence A002532 A098518 A086511
Adjacent sequences: A109185 A109186 A109187 this_sequence A109189 A109190 A109191
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2005
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