A138893 A generalized Chamberland function.

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, 425, 96, 443, 804, 461, 104, 479, 868, 497

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..55.

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;

Mathematica

LinearRecurrence[{2, -3, 4, -3, 2, -1}, {0, 11, 36, 29, 8, 47}, 56] (* or *) CoefficientList[Series[x(11+14x-10x^2+14x^3+7x^4)/((1-x)^2(1+x^2)^2), {x, 0, 55}], x] (* James C. McMahon, Jun 24 2025 *)

Crossrefs

Cf. A138894.

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

Extensions

a(47)-a(55) from James C. McMahon, Jun 24 2025

Status

approved