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Search: id:A089140
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| A089140 |
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Number of subsequences of {1,2,3,...,n} which are p_1-sequences. |
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+0
1
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| 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
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1,1
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COMMENT
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A p_k-sequence {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,...,n-1, where f is a polynomial of degree k with integer coefficients.
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REFERENCES
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John W. Layman and Bruce Landman, Note on the local growth of iterated polynomials, Aeq. Math. 27 (1984), 150-156.
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EXAMPLE
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{1,2,5,14} is a p_1-subsequence 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)=3x-1.
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CROSSREFS
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Sequence in context: A026474 A082562 A159243 this_sequence A000125 A129961 A133551
Adjacent sequences: A089137 A089138 A089139 this_sequence A089141 A089142 A089143
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Dec 05 2003
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