A390310 a(n) = if(n mod 3 = 0, n/3, 4 * n + (-1)^(n mod 3)).

0, 3, 9, 1, 15, 21, 2, 27, 33, 3, 39, 45, 4, 51, 57, 5, 63, 69, 6, 75, 81, 7, 87, 93, 8, 99, 105, 9, 111, 117, 10, 123, 129, 11, 135, 141, 12, 147, 153, 13, 159, 165, 14, 171, 177, 15, 183, 189, 16, 195, 201, 17, 207, 213, 18, 219, 225, 19, 231, 237, 20, 243, 249, 21, 255, 261, 22, 267, 273, 23, 279, 285, 24, 291, 297, 25

Offset

0,2

Comments

Does iterating n -> a(n) always reach 1 (i.e., cycle 1 -> 3 -> 1)?

Links

Table of n, a(n) for n=0..75.

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Formula

a(3*n) = n.

a(3*n+1) = a(3*n-2) + 12 for n > 0.

a(3*n+2) = a(3*n-1) + 12 for n > 0.

a(n) = 2 * a(n-3) - a(n-6) for n > 5.

G.f.: x*(3 + 9*x + x^2 + 9*x^3 + 3*x^4) / (1 - x^3)^2.

E.g.f.: exp(-x/2)*(25*exp(3*x/2)*x + 11*x*cos(sqrt(3)*x/2) + sqrt(3)*(11*x - 6)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, Nov 30 2025

Mathematica

a[n_] := If[Divisible[n, 3], n/3, 4*n + (-1)^Mod[n, 3]]; Array[a, 100, 0] (* Amiram Eldar, Nov 30 2025 *)

Prog

(PARI) a(n) = if(n%3 == 0, n/3, 4*n + (-1)^(n%3))

Crossrefs

Cf. A006370.

Sequence in context: A019817 A243526 A329214 * A080322 A126179 A304249

Adjacent sequences: A390307 A390308 A390309 * A390311 A390312 A390313

Keyword

nonn,easy

Author

Werner Schulte, Nov 30 2025

Status

approved