A128054 List the nonnegative integers where multiples of 6 occur twice and numbers of the form 6k+4 are omitted.

0, 0, 1, 2, 3, 5, 6, 6, 7, 8, 9, 11, 12, 12, 13, 14, 15, 17, 18, 18, 19, 20, 21, 23, 24, 24, 25, 26, 27, 29, 30, 30, 31, 32, 33, 35, 36, 36, 37, 38, 39, 41, 42, 42, 43, 44, 45, 47, 48, 48, 49, 50, 51, 53, 54, 54, 55, 56, 57, 59, 60, 60, 61, 62, 63, 65, 66, 66

Offset: 0

Author

Paul Barry, Feb 13 2007

Keywords

• easy
• nonn

Links

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

Programs

Mathematica

fix[n_]:=Which[Divisible[n,6],{n,n},Mod[n,6]==4,{},True,n]; Flatten[ fix/@ Range[0,70]] (* Harvey P. Dale, Aug 21 2014 *)

Formula

a(n) = a(n-6) + 6, for n >= 6.

a(n) = cos(2*Pi*n/3)/6-sqrt(3)*sin(2*Pi*n/3)/6+cos(Pi*n/3)/2-sqrt(3)*sin(Pi*n/3)/6+(3n-2)/3.

G.f.: x^2*(x^3+x^2+1) / ((x-1)^2*(x^2-x+1)*(x^2+x+1)). - Colin Barker, Jun 27 2013

Sum_{n>=2} (-1)^n/a(n) = 5*Pi/(12*sqrt(3)) - log(3)/4 + log(2)/3. - Amiram Eldar, Apr 04 2023