A140282 Numbers k such that A000330(k) is multiple of 3.

0, 4, 8, 9, 13, 17, 18, 22, 26, 27, 31, 35, 36, 40, 44, 45, 49, 53, 54, 58, 62, 63, 67, 71, 72, 76, 80, 81, 85, 89, 90, 94, 98, 99, 103, 107, 108, 112, 116, 117, 121, 125, 126, 130, 134, 135, 139, 143, 144, 148, 152, 153, 157, 161, 162, 166, 170, 171, 175, 179, 180, 184

Offset: 0

Author

Zak Seidov, May 23 2008

Keywords

• nonn
• easy

Comments

k mod 3 is periodic: 0,1,2, 0,1,2, 0,1,2, 0,1,2, 0,1,2, 0,1,2.

Links

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

Crossrefs

Cf. A000330.

Programs

Maple

seq(3*(n-floor(n/3)) +n, n= 0..61); # Gary Detlefs, Mar 27 2010

Mathematica

s={};Do[If[Mod[m*(1+m)*(1+2*m),18]==0,s={s,m}],{m,0,400}];Flatten[s]
Flatten[Position[Accumulate[Range[0,200]^2],?(Mod[#,3]==0&)]]-1 (* or *) LinearRecurrence[{1,0,1,-1},{0,4,8,9},100] (* _Harvey P. Dale, Mar 08 2018 *)

Formula

k*(1 + k)*(1 + 2*k) is multiple of 18; a(0..2)=0,4,8; a(n) = a(n-3) + 9 for n > 2.

a(n) = 3*(n-floor(n/3)) + n. - Gary Detlefs, Mar 27 2010

a(n) = 3*n + A010872(n). - Wesley Ivan Hurt, Jul 07 2013

G.f.: x*(x+2)^2 / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Jul 13 2013