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

0,4

Links

Table of n, a(n) for n=0..67.

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

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

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 *)

Crossrefs

Sequence in context: A165083 A165085 A309560 * A175081 A023834 A084735

Adjacent sequences: A128051 A128052 A128053 * A128055 A128056 A128057

Keyword

easy,nonn

Author

Paul Barry, Feb 13 2007

Status

approved