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

Author

Paul Barry, Apr 02 2008

Keywords

• easy
• nonn

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

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

Crossrefs

Cf. A138894.

Programs

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 *)

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;

Extensions

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