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Search: id:A108427
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| A108427 |
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Number of peaks of the form Ud in all paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1). |
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3
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| 1, 9, 85, 833, 8361, 85305, 880685, 9173505, 96220561, 1014889769, 10753517061, 114375683009, 1220435354425, 13058529727833, 140059477112925, 1505357362548737, 16209464357137953, 174827809500822345
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Problem 10658, American Math. Monthly, 107, 2000, 368-370.
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FORMULA
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a(n)=(1/n)sum(k*binomial(n, k)*binomial(3n-k, n-1), k=0..n).
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EXAMPLE
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a(2)=9 because we have ud(Ud)d, u(Ud)dd, (Ud)dud, (Ud)d(Ud)d, (Ud)udd, (Ud)(Ud)dd, U(Ud)ddd (the peaks of the form Ud shown between parentheses).
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MAPLE
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seq(add(k*binomial(n, k)*binomial(3*n-k, n-1)/n, k=0..n), n=1..22);
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CROSSREFS
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Cf. A027307, A108426.
Sequence in context: A015580 A163308 A160112 this_sequence A152106 A142982 A029711
Adjacent sequences: A108424 A108425 A108426 this_sequence A108428 A108429 A108430
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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), Jun 03 2005
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