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A126223
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Number of level steps in all 2-Motzkin paths (i.e. Motzkin paths with blue and red level steps) of length n, without red level steps on the x-axis.
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1
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0, 1, 2, 7, 26, 98, 372, 1419, 5434, 20878, 80444, 310726, 1202852, 4665412, 18126760, 70538355, 274877370, 1072515990, 4189573740, 16383007410, 64126407180, 251226790620, 985033185240, 3865138313790, 15176957307876
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = Sum(k*A126222(n,k), k=0..n).
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FORMULA
| G.f.: (1-2z)[1-2z-sqrt(1-4*z)]/[2z*sqrt(1-4z)].
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EXAMPLE
| a(3) = 7 because the 2-Motzkin paths without red level steps on the x-axis are BBB, BUD, UBD, URD and UDB, where U=(1,1), D=(1,-1), B=blue (1,0), R=red (1,0); they have a total of 3+1+1+1+1 =7 level steps.
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MAPLE
| G:=(1-2*z)*(1-2*z-sqrt(1-4*z))/2/z/sqrt(1-4*z): Gser:=series(G, z=0, 32): seq(coeff(Gser, z, n), n=0..28);
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CROSSREFS
| Cf. A126222.
Sequence in context: A055988 A001075 A113436 * A114121 A049775 A101850
Adjacent sequences: A126220 A126221 A126222 * A126224 A126225 A126226
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 28 2006
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