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%I #11 Sep 08 2015 17:29:56
%S 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,
%T 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,
%U 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
%N a(n) is the number of distinct n-th powers of functions {1, 2} -> {1, 2}.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1).
%F For n > 2, a(n) = a(n-2).
%F G.f.: (1+4*x+2*x^2)/(1-x^2). - _Jaume Oliver Lafont_, Mar 20 2009
%e 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.
%t Join[{1},LinearRecurrence[{0, 1},{4, 3},104]] (* _Ray Chandler_, Sep 08 2015 *)
%Y Cf. A102687, A102709, A103948-A103950.
%Y Cf. A158515. - _Jaume Oliver Lafont_, Mar 20 2009
%Y Row n=2 of A247026.
%K easy,nonn
%O 0,2
%A _David Wasserman_, Feb 21 2005
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