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Search: id:A057586
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| A057586 |
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Area under Motzkin paths. |
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+0
2
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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; listen)
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OFFSET
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1,2
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COMMENT
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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
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C. Banderier, Analytic combinatorics of random walks and planar maps, PhD Thesis, 2001.
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FORMULA
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-(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^2)
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CROSSREFS
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Sequence in context: A053347 A036600 A058645 this_sequence A139610 A088404 A119334
Adjacent sequences: A057583 A057584 A057585 this_sequence A057587 A057588 A057589
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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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