A103947 a(n) is the number of distinct n-th powers of functions {1, 2} -> {1, 2}.

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

Offset: 0

Author

David Wasserman, Feb 21 2005

Keywords

• easy
• nonn

Examples

			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.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1).

Crossrefs

Cf. A102687, A102709, A103948, A103949, A103950.

Cf. A158515.

Row n=2 of A247026.

Programs

Mathematica

Join[{1},LinearRecurrence[{0, 1},{4, 3},104]] (* Ray Chandler, Sep 08 2015 *)

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

a(n) = (n mod 2)+(2 mod (n+2))+1. - Aaron J Grech, Sep 02 2024

E.g.f.: 3*cosh(x) + 4*sinh(x) - 2. - Stefano Spezia, Sep 04 2024