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A103947
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a(n) is the number of distinct n-th powers of functions {1, 2} -> {1, 2}.
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4
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1, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..104.
Index entries for linear recurrences with constant coefficients, signature (0, 1).
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FORMULA
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For n > 2, a(n) = a(n-2).
G.f.: (1+4*x+2*x^2)/(1-x^2). - Jaume Oliver Lafont, Mar 20 2009
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EXAMPLE
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a(4) = 3: the four functions {1, 2} -> {1, 2} are f(x) = 1, g(x) = 2, h(x) = x and j(x) = 3 - x. f^4(x) = f(f(f(f(x)))) = 1; so f^4 = f. Similarly, g^4 = g, h^4 = h and j^4 = h, so there are 3 distinct 4th powers.
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MATHEMATICA
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Join[{1}, LinearRecurrence[{0, 1}, {4, 3}, 104]] (* Ray Chandler, Sep 08 2015 *)
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CROSSREFS
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Cf. A102687, A102709, A103948-A103950.
Cf. A158515. - Jaume Oliver Lafont, Mar 20 2009
Row n=2 of A247026.
Sequence in context: A171783 A251767 A168309 * A178038 A241928 A111048
Adjacent sequences: A103944 A103945 A103946 * A103948 A103949 A103950
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KEYWORD
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easy,nonn
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AUTHOR
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David Wasserman, Feb 21 2005
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STATUS
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approved
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