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Search: id:A057585
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| A057585 |
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Area under Motzkin excursions. |
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+0
2
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| 0, 1, 4, 16, 56, 190, 624, 2014, 6412, 20219, 63284, 196938, 610052, 1882717, 5792528, 17776102, 54433100, 166374109, 507710420, 1547195902, 4709218604, 14318240578, 43493134160, 132003957436, 400337992056, 1213314272395
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) is the sum of areas under all Motzkin excursions of length n. (nonnegative walks beginning and ending in 0, with jumps -1,0,+1)
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..400
C. Banderier, Analytic combinatorics of random walks and planar maps, PhD Thesis, 2001.
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FORMULA
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G.f.=(x^2+2*x-1+(-x+1)*sqrt((x+1)*(1-3*x)))/(2*(3*x-1)*(x+1)*x^2)
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MAPLE
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G:= (x^2+2*x-1+(-x+1)*sqrt((x+1)*(1-3*x)))/(2*(3*x-1)*(x+1)*x^2): Gser:=series(G, x=0, 30): seq(coeff(Gser, x, n), n=1..26); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 08 2007
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CROSSREFS
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Sequence in context: A026126 A026155 A025182 this_sequence A097128 A006079 A122032
Adjacent sequences: A057582 A057583 A057584 this_sequence A057586 A057587 A057588
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Cyril Banderier (Cyril.Banderier(AT)inria.fr), Oct 04 2000
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