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Search: id:A089383
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| A089383 |
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Number of peaks at even level in all Schroeder paths (i.e. consisting of steps U=(1,1), D=(1,-1), H=(2,0) and never going below the axis) from (0,0) to (2n+4,0). |
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+0
1
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| 1, 8, 49, 280, 1569, 8752, 48833, 272976, 1529441, 8589176, 48342449, 272640680, 1540495553, 8718956768, 49423735553, 280551815456, 1594568513857, 9073566717800, 51686272315569, 294711466792120, 1681938025818081
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Partial sums of A026002.
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FORMULA
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G.f.=(1-z-q)^2/[4z^2(1-z)q], where q = sqrt(1-6z+z^2).
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EXAMPLE
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a(0)=1 because the paths HH, HUD, UDH, UHD, UDUD and U(UD)D from (0,0) to (4,0) have only one peak at an even level (shown between parentheses).
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CROSSREFS
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Cf. A006318.
Adjacent sequences: A089380 A089381 A089382 this_sequence A089384 A089385 A089386
Sequence in context: A005059 A026719 A026774 this_sequence A028443 A001108 A097204
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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), Dec 28 2003
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