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A080839 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,...}. 0
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

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, Feb 05 2007

LINKS

Table of n, a(n) for n=1..13.

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. A036262.

Cf. 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

Adjacent sequences:  A080836 A080837 A080838 * A080840 A080841 A080842

KEYWORD

nonn

AUTHOR

John W. Layman, Mar 28 2003

EXTENSIONS

More terms from T. D. Noe, Feb 05 2007

STATUS

approved

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Last modified November 17 01:05 EST 2019. Contains 329209 sequences. (Running on oeis4.)