A088439 a(3n) = 3n, otherwise a(n) = 1.

0, 1, 1, 3, 1, 1, 6, 1, 1, 9, 1, 1, 12, 1, 1, 15, 1, 1, 18, 1, 1, 21, 1, 1, 24, 1, 1, 27, 1, 1, 30, 1, 1, 33, 1, 1, 36, 1, 1, 39, 1, 1, 42, 1, 1, 45, 1, 1, 48, 1, 1, 51, 1, 1, 54, 1, 1, 57, 1, 1, 60, 1, 1, 63, 1, 1, 66, 1, 1, 69, 1, 1, 72, 1, 1, 75, 1, 1, 78, 1, 1, 81, 1, 1, 84, 1, 1, 87, 1, 1, 90, 1, 1

Offset: 0

Author

Roger L. Bagula, Nov 09 2003

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Crossrefs

Cf. A011655, A079978, A088440, A175676, A124625.

Programs

Magma

[n mod 3 eq 0 select n else 1: n in [0..100]];  // Bruno Berselli, Mar 11 2011

Mathematica

Table[If[Divisible[n,3],n,1],{n,0,100}] (* or *) LinearRecurrence[ {0,0,2,0,0,-1},{0,1,1,3,1,1},100] (* Harvey P. Dale, Jun 18 2018 *)

SageMath

def A088439(n): return 1 if (n%3) else n
[A088439(n) for n in range(121)] # G. C. Greubel, Dec 05 2022

Formula

From Bruno Berselli, Mar 11 2011: (Start)

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

a(n) = n^A079978(n).

a(n) = 3*A175676(n-1) + A011655(n) for n>0. (End)

E.g.f.: (1/3)*(x+2)*exp(x) - (2/3)*exp(-x/2)*( cos(sqrt(3)*x/2) + x*sin((Pi + 3*sqrt(3)*x)/6) ). - G. C. Greubel, Dec 05 2022