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A057586
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Area under Motzkin paths.
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1
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1, 10, 54, 242, 979, 3728, 13627, 48382, 168069, 574040, 1934346, 6446824, 21290563, 69771854, 227150074, 735316478, 2368536349, 7596077384, 24267094264, 77258501372, 245204480443, 776060212130, 2449968185161
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) is 2*the sum of areas under all Motzkin excursions of length n. (nonnegative walks beginning in 0, with jumps -1,0,+1)
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LINKS
| C. Banderier, Analytic combinatorics of random walks and planar maps, PhD Thesis, 2001.
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FORMULA
| G.f.: -(3*x^3-x^2-7*x+1+sqrt((x+1)*(1-3*x))*(3*x^2+6*x-1)) / (2*(x+1) * (3*x-1)^2*x).
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MATHEMATICA
| f[x_] := -2*(3*x^3-x^2-7*x+1+Sqrt[(x+1)*(1-3*x)]*(3*x^2+6*x-1)) / (4*(x+1)*(3*x-1)^2*x); CoefficientList[ Series[ f[x], {x, 1, 23}], x] (* From Jean-François Alcover, Dec 21 2011, from area sum g.f. *)
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CROSSREFS
| Sequence in context: A036600 A058645 A170940 * A198770 A139610 A088404
Adjacent sequences: A057583 A057584 A057585 * A057587 A057588 A057589
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Cyril Banderier (Cyril.Banderier(AT)inria.fr), Oct 04 2000
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