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Search: id:A054542
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| A054542 |
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A Catalan-like sequence. |
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+0
2
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| 1, 2, 4, 12, 36, 116, 382, 1287, 4420, 15397, 54264, 193154, 693374, 2507288, 9124560, 33393355, 122821380, 453756765, 1683107800, 6265751310, 23402516280, 87670790155, 329337229104, 1240292449350, 4681874312510
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This sequence (k=2, p=2) belongs to a family of Catalan-like sequences that merit further investigation. The ceiling is taken in order to eliminate the fractional parts. Are there combinations of k and p for which the ceiling is unnecessary?
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REFERENCES
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Felix Goldberg, A problem relating to a family of Catalan-like sequences, forthcoming.
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FORMULA
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a(n) = Ceiling ( 1/(n+k)*C(pn, n) ), where k=2, p=2 (in the standard Catalan sequence k=1 and p=2).
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EXAMPLE
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a(6)=116 because 1/(6+2)*C(12,6) is 115.5 and taking the ceiling we obtain 116.
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CROSSREFS
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Cf. A000108.
Sequence in context: A149841 A149842 A149843 this_sequence A117757 A009623 A148208
Adjacent sequences: A054539 A054540 A054541 this_sequence A054543 A054544 A054545
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KEYWORD
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nonn
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AUTHOR
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Felix Goldberg (sgefelix(AT)t2.technion.ac.il), Apr 10 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 11 2000
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