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A103947 a(n) is the number of distinct n-th powers of functions {1, 2} -> {1, 2}. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
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
EXAMPLE
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.
MATHEMATICA
Join[{1}, LinearRecurrence[{0, 1}, {4, 3}, 104]] (* Ray Chandler, Sep 08 2015 *)
CROSSREFS
Cf. A158515. - Jaume Oliver Lafont, Mar 20 2009
Row n=2 of A247026.
Sequence in context: A171783 A251767 A168309 * A178038 A241928 A111048
KEYWORD
easy,nonn
AUTHOR
David Wasserman, Feb 21 2005
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)