

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
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OFFSET

1,4


COMMENTS

The slowestgrowing sequence of length n is 1,2,4,6,...,2(n1). The fastestgrowing sequence is 1,2,4,8,...,2^(n1). The ratio a(n+1)a(n1)/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



