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A080839
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Number of increasing integer sequences of length n with Gilbreath transform (that is, the diagonal of leading successive absolute differences) given by {1,1,1,1,1,...}.
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0
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1, 1, 1, 2, 6, 27, 180, 1786, 26094, 559127, 17535396, 804131875, 53833201737
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The slowest-growing sequence of length n is 1,2,4,6,...,2(n-1). The fastest-growing sequence is 1,2,4,8,...,2^(n-1). The ratio a(n+1)a(n-1)/a(n)^2 appears to converge to a constant near 1.46, which is the approximate growth rate of A001609. Are the sequences related? - T. D. Noe (noe(AT)sspectra.com), Feb 05 2007
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EXAMPLE
| The table below shows that {1,2,4,6,10} is one of the 6 sequences of length 5 that satisfy the stated condition:
1
2 1
4 2 1
6 2 0 1
10 4 2 2 1
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CROSSREFS
| Cf. A036262.
Cf. A136465, the total number of increasing sequences with the same maximum length. [From Charles R Greathouse IV (charles.greathouse(AT)case.edu), Aug 08 2010]
Sequence in context: A070076 A130455 A005270 * A118085 A011834 A003513
Adjacent sequences: A080836 A080837 A080838 * A080840 A080841 A080842
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Mar 28 2003
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EXTENSIONS
| More terms from T. D. Noe (noe(AT)sspectra.com), Feb 05 2007
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