

A089140


Number of subsequences of {1,2,3,...,n} which are p_1sequences.


1



2, 4, 8, 15, 26, 40, 60, 84, 114, 149, 190, 234, 288, 346, 411, 484, 565, 649, 743, 840, 947, 1063, 1185
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OFFSET

1,1


COMMENTS

A p_ksequence {x(i)} is one which is strictly monotone increasing,i.e. x(i+1)>x(i) for i=1,2,3,...,n and satisfies the condition that a(k+1)=f(a(k)), for k=1,2,3,...,n1, where f is a polynomial of degree k with integer coefficients.


REFERENCES

John W. Layman and Bruce Landman, Note on the local growth of iterated polynomials, Aeq. Math. 27 (1984), 150156.


LINKS

Table of n, a(n) for n=1..23.


EXAMPLE

{1,2,5,14} is a p_1subsequence of {1,2,3,...,14}, since 2=f(1), 5=f(2) and 14=f(5) where f is the first degree polynomial given by f(x)=3x1.


CROSSREFS

Sequence in context: A325840 A324740 A262146 * A204555 A000125 A129961
Adjacent sequences: A089137 A089138 A089139 * A089141 A089142 A089143


KEYWORD

nonn


AUTHOR

John W. Layman, Dec 05 2003


STATUS

approved



