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Search: id:A125267
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| A125267 |
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Number of Motzkin paths with no peaks and with level steps at height 0 having three colors except that consecutive level steps at height 0 must have different colors. |
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+0
1
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| 1, 3, 6, 13, 30, 71, 171, 417, 1026, 2542, 6333
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This generating function, together with the multiplier function -xg(x), produce an involution in the Riordan group.
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REFERENCES
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N.T. Cameron and A. Nkwanta, On some (pseudo) involutions in the Riordan group, J. of Integer Sequences, 8(2005),1-16.
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FORMULA
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Generating function = (g(x)*(1+x))/(1-x*g(x)) where g(x)=((1-x+x^2)-sqrt((1-x+x^2)^2-4x^2)/(2*x^2)
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EXAMPLE
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a(3) = 13 since there are 12 = 3*2*2 paths that stay at level 0 and one path ULD that goes above level 0.
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CROSSREFS
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Cf. A004148.
Adjacent sequences: A125264 A125265 A125266 this_sequence A125268 A125269 A125270
Sequence in context: A087218 A098075 A137584 this_sequence A141353 A130582 A126296
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KEYWORD
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nonn
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AUTHOR
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Louis Shapiro and Gi-Sang Cheon (lshapiro(AT)howard.edu), Jan 15 2007
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