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A140282
Numbers k such that A000330(k) is multiple of 3.
1
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
0,2
COMMENTS
k mod 3 is periodic: 0,1,2, 0,1,2, 0,1,2, 0,1,2, 0,1,2, 0,1,2.
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
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 *)
CROSSREFS
Cf. A000330.
Sequence in context: A308416 A010429 A376357 * A161757 A134376 A163408
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, May 23 2008
STATUS
approved