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A122880
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Catalan numbers minus odd indexed Fibonacci numbers.
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0
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0, 0, 0, 1, 8, 43, 196, 820, 3265, 12615, 47840, 179355, 667875, 2478022, 9180616, 34011401, 126120212, 468411235, 1743105373, 6500874434, 24300686879, 91049069203, 341924710480, 1286932932251, 4854167659403, 18346988061078
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 21 2008: (Start)
Number of Dyck paths of height at least 4 and of semilength n. Example: a(5)=8 because we have UUUUUDDDDD, UUUUDUDDDD, UUUDUUDDDD, UUDUUUDDDD, UDUUUUDDDD and the reflection of the last three in a vertical axis.
Number of ordered trees of height at least 4 and having n edges. (End)
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REFERENCES
| E. Deutsch and H. Prodinger, A bijection between directed column-convex polyominoes and ordered trees of height at most three, Theoretical Comp. Science, 307, 2003, 319-325. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 21 2008]
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FORMULA
| A000108(n) - A001519(n), n>0; A000108 = Catalan numbers, A001519 = odd indexed Fibonacci numbers.
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EXAMPLE
| a(5) = 8 = A000108(5) - A001519(5) = 42 - 34.
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MAPLE
| with(combinat): seq(binomial(2*n, n)/(n+1)-fibonacci(2*n-1), n=1..27); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 21 2008]
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CROSSREFS
| Cf. A122881.
Sequence in context: A137748 A005024 A094865 * A171479 A099253 A034361
Adjacent sequences: A122877 A122878 A122879 * A122881 A122882 A122883
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 16 2006
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 21 2008
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