

A103947


a(n) is the number of distinct nth 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
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..104.
Index entries for linear recurrences with constant coefficients, signature (0, 1).


FORMULA

For n > 2, a(n) = a(n2).
G.f.: (1+4*x+2*x^2)/(1x^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. A102687, A102709, A103948A103950.
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


KEYWORD

easy,nonn


AUTHOR

David Wasserman, Feb 21 2005


STATUS

approved



