A128054 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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