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A138893 A generalized Chamberland function. 1
0, 11, 36, 29, 8, 47, 100, 65, 16, 83, 164, 101, 24, 119, 228, 137, 32, 155, 292, 173, 40, 191, 356, 209, 48, 227, 420, 245, 56, 263, 484, 281, 64, 299, 548, 317, 72, 335, 612, 353, 80, 371, 676, 389, 88, 407, 740 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The orbit of a(n) beginning at 1 is A138894.

REFERENCES

M. Chamberland, A Continuous Extension of the 3x+1 Problem to the Real Line, Dynamics of Continuous, Discrete and Impulsive Dynamical Systems 2(1996), 495-509

LINKS

Table of n, a(n) for n=0..46.

Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-3,2,-1).

FORMULA

G.f.: x(11+14x-10x^2+14x^3+7x^4)/((1-x)^2(1+x^2)^2);

a(n)=9n+2-(7n+2)cos(pi*n/2);

a(n)=6((n/3)*(cos(pi*n/4))^2+(2/3)*(4n+1)*(sin(pi*n/4))^2);

a(4n)=8n; a(4n+1)=11+36n; a(4n+2)=4*(9+16n); a(4n+3)=29+36n;

CROSSREFS

Sequence in context: A123749 A159493 A012644 * A243151 A225130 A191292

Adjacent sequences: A138890 A138891 A138892 * A138894 A138895 A138896

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 02 2008

STATUS

approved

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Last modified February 7 17:57 EST 2023. Contains 360128 sequences. (Running on oeis4.)