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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 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. A001609, A036262, A363002, A363003, A363004, A363005. 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 Adjacent sequences: A080836 A080837 A080838 * A080840 A080841 A080842 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.)