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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

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(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. A102687, A102709, A103948-A103950.

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

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Last modified January 15 19:32 EST 2021. Contains 340189 sequences. (Running on oeis4.)