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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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2
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1, 9, 85, 833, 8361, 85305, 880685, 9173505, 96220561, 1014889769, 10753517061, 114375683009, 1220435354425, 13058529727833, 140059477112925, 1505357362548737, 16209464357137953, 174827809500822345
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Problem 10658, American Math. Monthly, 107, 2000, 368-370.
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FORMULA
| a(n)=(1/n)sum(k*binomial(n, k)*binomial(3n-k, n-1), k=0..n).
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EXAMPLE
| 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
| seq(add(k*binomial(n, k)*binomial(3*n-k, n-1)/n, k=0..n), n=1..22);
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CROSSREFS
| Cf. A027307, A108426.
Sequence in context: A015580 A163308 A160112 * A152106 A142982 A196955
Adjacent sequences: A108424 A108425 A108426 * A108428 A108429 A108430
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 03 2005
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