This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A103947 #23 Sep 04 2024 14:12:32
%S A103947 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 A103947 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 A103947 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 A103947 a(n) is the number of distinct n-th powers of functions {1, 2} -> {1, 2}.
%H A103947 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A103947 For n > 2, a(n) = a(n-2).
%F A103947 G.f.: (1+4*x+2*x^2)/(1-x^2). - _Jaume Oliver Lafont_, Mar 20 2009
%F A103947 a(n) = (n mod 2)+(2 mod (n+2))+1. - _Aaron J Grech_, Sep 02 2024
%F A103947 E.g.f.: 3*cosh(x) + 4*sinh(x) - 2. - _Stefano Spezia_, Sep 04 2024
%e A103947 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 A103947 Join[{1},LinearRecurrence[{0, 1},{4, 3},104]] (* _Ray Chandler_, Sep 08 2015 *)
%Y A103947 Cf. A102687, A102709, A103948, A103949, A103950.
%Y A103947 Cf. A158515.
%Y A103947 Row n=2 of A247026.
%K A103947 easy,nonn
%O A103947 0,2
%A A103947 _David Wasserman_, Feb 21 2005