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A080839 Number of positive 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,...}. 4
1, 1, 1, 2, 6, 27, 180, 1786, 26094, 559127, 17535396, 804131875, 53833201737 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
From T. D. Noe, Feb 05 2007: (Start)
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?
(End)
Also, a(n) is the number of (not necessarily increasing) positive integer sequences of length n-1 with Gilbreath transform (1, ..., 1). - Pontus von Brömssen, May 13 2023
LINKS
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
CROSSREFS
Cf. also A136465, the total number of increasing sequences with the same maximum length. [From Charles R Greathouse IV, Aug 08 2010]
Sequence in context: A005270 A308444 A277611 * A118085 A058712 A011834
KEYWORD
nonn,more
AUTHOR
John W. Layman, Mar 28 2003
EXTENSIONS
More terms from T. D. Noe, Feb 05 2007
Added "positive" to definition. - N. J. A. Sloane, May 13 2023
STATUS
approved

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Last modified February 20 21:52 EST 2024. Contains 370219 sequences. (Running on oeis4.)