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Search: id:A026135
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| A026135 |
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Number of (s(0),s(1),...,s(n)) such that every s(i) is a nonnegative integer, s(0) = 1, |s(1) - s(0)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also sum of numbers in row n+1 of the array T defined in A026120. |
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4
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| 1, 2, 5, 14, 39, 110, 312, 890, 2550, 7334, 21161, 61226, 177575, 516114, 1502867, 4383462, 12804429, 37452870, 109682319, 321564658, 943701141, 2772060618, 8149661730, 23978203662, 70600640796, 208014215066, 613266903927
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is the total number of rows of consecutive peaks in all Motzkin (n+2)-paths. For example, with U=upstep, D=downstep, F=flatstep, the path FU(UD)FU(UDUDUD)DD(UD) contains 3 rows of peaks (in parentheses). The 9 Motzkin 4-paths are FFFF, FF(UD), F(UD)F, FUFD, (UD)FF, (UDUD), UFDF, UFFD, U(UD)D, containing a total of 5 rows of peaks and so a(2)=5. - David Callan (callan(AT)stat.wisc.edu), Aug 16 2006
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FORMULA
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a(n) = Sum_{k=0..n} binomial(n-1, k-1)*binomial(k+1, floor((k+1)/2)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 18 2003
G.f. ((x-1)^2*((1+x)/(1-3x))^(1/2) + x^2 - 1)/(2*x^2). - David Callan (callan(AT)stat.wisc.edu), Aug 16 2006
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CROSSREFS
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First differences are in A025566, second differences in A005773.
Pairwise sums of A025179.
Sequence in context: A001011 A132834 A000641 this_sequence A105641 A027035 A102406
Adjacent sequences: A026132 A026133 A026134 this_sequence A026136 A026137 A026138
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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More terms from David Callan (callan(AT)stat.wisc.edu), Aug 16 2006
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